Probability, Statistics, and Justice
Jeffrey S. Rosenthal
Professor Department of Statistics University of Toronto jeff@math.toronto.edu www.probability.ca
(Canadian Institute for the Administration of Justice, Annual Conference, October 10, 2013)
(1/45) I’m a Professor of Statistics. A typical day’s work:
Therefore √ − (d) + (d) α (βi ) = α (βi − `/ d)
1/2 (d) 1/2 (d) 0 1/2 (d) 000 (d) d + (d) (`(βi )I (βi )) −` I (βi )` `K (βi ) ≈ α (βi )− √ φ − − 2 2 1/2 (d) d 6I (βi ) (d) 1/2 (d) 0 2 (d) 000 (`(βi )I (βi )) −` − exp(−` (β )K (βi )/6) √ × i 2 d I 1/2(β(d))` `K 000(β(d)) ×φ − i + i 2 1/2 (d) 6I (βi ) 1/2 1/2 d d 0 Then, since ` ≈ ` + `0 ≈ ` + `0 = ` + `` , we have that d1/2
0 d1/2 1 h `` µ(β(d)) ≈ − α+` + ` + × i 2d 1/2 d 1/2
(d) 1/2 (d) 0 1/2 (d) 000 (d) + (d) (`(βi )I (βi )) −` I (βi )` `K (βi ) α (βi )− √ φ − − − 2 2 1/2 (d) d 6I (βi )
About Me . . .
(2/45) A typical day’s work:
Therefore √ − (d) + (d) α (βi ) = α (βi − `/ d)
1/2 (d) 1/2 (d) 0 1/2 (d) 000 (d) d + (d) (`(βi )I (βi )) −` I (βi )` `K (βi ) ≈ α (βi )− √ φ − − 2 2 1/2 (d) d 6I (βi ) (d) 1/2 (d) 0 2 (d) 000 (`(βi )I (βi )) −` − exp(−` (β )K (βi )/6) √ × i 2 d I 1/2(β(d))` `K 000(β(d)) ×φ − i + i 2 1/2 (d) 6I (βi ) 1/2 1/2 d d 0 Then, since ` ≈ ` + `0 ≈ ` + `0 = ` + `` , we have that d1/2
0 d1/2 1 h `` µ(β(d)) ≈ − α+` + ` + × i 2d 1/2 d 1/2
(d) 1/2 (d) 0 1/2 (d) 000 (d) + (d) (`(βi )I (βi )) −` I (βi )` `K (βi ) α (βi )− √ φ − − − 2 2 1/2 (d) d 6I (βi )
About Me . . . I’m a Professor of Statistics.
(2/45) Therefore √ − (d) + (d) α (βi ) = α (βi − `/ d)
1/2 (d) 1/2 (d) 0 1/2 (d) 000 (d) d + (d) (`(βi )I (βi )) −` I (βi )` `K (βi ) ≈ α (βi )− √ φ − − 2 2 1/2 (d) d 6I (βi ) (d) 1/2 (d) 0 2 (d) 000 (`(βi )I (βi )) −` − exp(−` (β )K (βi )/6) √ × i 2 d I 1/2(β(d))` `K 000(β(d)) ×φ − i + i 2 1/2 (d) 6I (βi ) 1/2 1/2 d d 0 Then, since ` ≈ ` + `0 ≈ ` + `0 = ` + `` , we have that d1/2
0 d1/2 1 h `` µ(β(d)) ≈ − α+` + ` + × i 2d 1/2 d 1/2
(d) 1/2 (d) 0 1/2 (d) 000 (d) + (d) (`(βi )I (βi )) −` I (βi )` `K (βi ) α (βi )− √ φ − − − 2 2 1/2 (d) d 6I (βi )
About Me . . . I’m a Professor of Statistics. A typical day’s work:
(2/45) About Me . . . I’m a Professor of Statistics. A typical day’s work:
Therefore √ − (d) + (d) α (βi ) = α (βi − `/ d)
1/2 (d) 1/2 (d) 0 1/2 (d) 000 (d) d + (d) (`(βi )I (βi )) −` I (βi )` `K (βi ) ≈ α (βi )− √ φ − − 2 2 1/2 (d) d 6I (βi ) (d) 1/2 (d) 0 2 (d) 000 (`(βi )I (βi )) −` − exp(−` (β )K (βi )/6) √ × i 2 d I 1/2(β(d))` `K 000(β(d)) ×φ − i + i 2 1/2 (d) 6I (βi ) 1/2 1/2 d d 0 Then, since ` ≈ ` + `0 ≈ ` + `0 = ` + `` , we have that d1/2
0 d1/2 1 h `` µ(β(d)) ≈ − α+` + ` + × i 2d 1/2 d 1/2
(d) 1/2 (d) 0 1/2 (d) 000 (d) + (d) (`(βi )I (βi )) −` I (βi )` `K (βi ) α (βi )− √ φ − − − 2 2 1/2 (d) d 6I (βi ) (2/45) And then one day I wrote a successful book . . .
(3/45) Opinion Polls . . .
Then I was interviewed by the media about:
(4/45) Then I was interviewed by the media about: Opinion Polls . . .
(4/45) Crime statistics . . .
(5/45) Pedestrian death counts...
(6/45) Making decisions . . .
(7/45) Game show strategies . . .
(8/45) The Maple Leafs . . .
To: [email protected] From: jeff@math.toronto.edu (Jeffrey Rosenthal) Date: Wed, 12 Apr 2006 16:11:08 -0400 (EDT) Subject: my calculations Hi Mike, good talking to you on the phone just now. I assumed that in each game, each team has probability 45% of getting two points, 10% of getting one point, and 45% of getting zero points. Those figures then lead to the following probabilities for Toronto to beat or tie each of the various other teams (in total points at end of season): Prob that Toronto beats Montreal = 0.17% Prob that Toronto ties Montreal = 0.30% Prob that Toronto ties Atlanta = 11.5% Prob that Toronto beats Atlanta = 30.2% Prob that Toronto ties Tampa Bay = 3.6% Prob that Toronto beats Tampa Bay = 2.1% * This gives a total probability of 5.8% (about one chance in 17) for Toronto to have a chance at the playoffs.
(9/45) And lotteries . . .
(10/45) . . . Lots of lotteries . . .
(11/45) Auric Goldfinger: “Once is happenstance. Twice is coincidence. The third time it’s enemy action.”
So what is the connection to JUSTICE?
(12/45) Auric Goldfinger: “Once is happenstance. Twice is coincidence. The third time it’s enemy action.”
So what is the connection to JUSTICE?
(12/45) “Once is happenstance. Twice is coincidence. The third time it’s enemy action.”
So what is the connection to JUSTICE?
Auric Goldfinger: (12/45) So what is the connection to JUSTICE?
Auric Goldfinger: “Once is happenstance. Twice is coincidence. The third time it’s enemy action.” (12/45) Statistics and Justice both involve evaluating evidence. Justice: “beyond a reasonable doubt” “balance of probabilities” “preponderance of the evidence” Statistics: “statistically significant” “the probability is more than X” “the p-value is less than Y” (“significant”?? “probability”?? “p-value”??) In this talk, I will try to: (a) explain how statistical reasoning works, and (b) illustrate why it must be used with caution.
Probability, Statistics . . . and Justice?
(13/45) Justice: “beyond a reasonable doubt” “balance of probabilities” “preponderance of the evidence” Statistics: “statistically significant” “the probability is more than X” “the p-value is less than Y” (“significant”?? “probability”?? “p-value”??) In this talk, I will try to: (a) explain how statistical reasoning works, and (b) illustrate why it must be used with caution.
Probability, Statistics . . . and Justice?
Statistics and Justice both involve evaluating evidence.
(13/45) Statistics: “statistically significant” “the probability is more than X” “the p-value is less than Y” (“significant”?? “probability”?? “p-value”??) In this talk, I will try to: (a) explain how statistical reasoning works, and (b) illustrate why it must be used with caution.
Probability, Statistics . . . and Justice?
Statistics and Justice both involve evaluating evidence. Justice: “beyond a reasonable doubt” “balance of probabilities” “preponderance of the evidence”
(13/45) (“significant”?? “probability”?? “p-value”??) In this talk, I will try to: (a) explain how statistical reasoning works, and (b) illustrate why it must be used with caution.
Probability, Statistics . . . and Justice?
Statistics and Justice both involve evaluating evidence. Justice: “beyond a reasonable doubt” “balance of probabilities” “preponderance of the evidence” Statistics: “statistically significant” “the probability is more than X” “the p-value is less than Y”
(13/45) In this talk, I will try to: (a) explain how statistical reasoning works, and (b) illustrate why it must be used with caution.
Probability, Statistics . . . and Justice?
Statistics and Justice both involve evaluating evidence. Justice: “beyond a reasonable doubt” “balance of probabilities” “preponderance of the evidence” Statistics: “statistically significant” “the probability is more than X” “the p-value is less than Y” (“significant”?? “probability”?? “p-value”??)
(13/45) (a) explain how statistical reasoning works, and (b) illustrate why it must be used with caution.
Probability, Statistics . . . and Justice?
Statistics and Justice both involve evaluating evidence. Justice: “beyond a reasonable doubt” “balance of probabilities” “preponderance of the evidence” Statistics: “statistically significant” “the probability is more than X” “the p-value is less than Y” (“significant”?? “probability”?? “p-value”??) In this talk, I will try to: (13/45) and (b) illustrate why it must be used with caution.
Probability, Statistics . . . and Justice?
Statistics and Justice both involve evaluating evidence. Justice: “beyond a reasonable doubt” “balance of probabilities” “preponderance of the evidence” Statistics: “statistically significant” “the probability is more than X” “the p-value is less than Y” (“significant”?? “probability”?? “p-value”??) In this talk, I will try to: (a) explain how statistical reasoning works, (13/45) Probability, Statistics . . . and Justice?
Statistics and Justice both involve evaluating evidence. Justice: “beyond a reasonable doubt” “balance of probabilities” “preponderance of the evidence” Statistics: “statistically significant” “the probability is more than X” “the p-value is less than Y” (“significant”?? “probability”?? “p-value”??) In this talk, I will try to: (a) explain how statistical reasoning works, and (b) illustrate why it must be used with caution. (13/45) Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence
(14/45) Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi?
(14/45) Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test!
(14/45) Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time.
(14/45) No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability?
(14/45) What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck!
(14/45) three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row?
(14/45) ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times?
(14/45) The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times?
(14/45) • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random.
(14/45) 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value =
(14/45) • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%.
(14/45) (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value =
(14/45) • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%.
(14/45) multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row:
(14/45) (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply
(14/45) . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”):
(14/45) The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%.
(14/45) the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value,
(14/45) Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something.
(14/45) “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard:
(14/45) For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20).
(14/45) two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi:
(14/45) five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant,
(14/45) Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
(14/45) Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly:
(14/45) New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate.
(14/45) does it work? If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug:
(14/45) If it saves 5 patients in a row, then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work?
(14/45) then yes it’s “significant”!
How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, (14/45) How Statisticians Weigh Evidence Example: Can your friend distinguish Coke from Pepsi? Do a test! Guesses right the first time. Proof of ability? No, could be luck! What about twice in a row? three times? ten times? The p-value is the probability of such a result if it’s just random. • Guess right once: p-value = 1/2 = 50%. • Guess right twice in a row: p-value = (1/2) × (1/2) = 25%. • Guess right five times in a row: multiply (“independent”): . p-value = (1/2) × (1/2) × (1/2) × (1/2) × (1/2) = 3.1%. The smaller the p-value, the more it seems to “prove” something. Usual standard: “significant” if p-value less than 5% (i.e., 1 in 20). For Coke versus Pepsi: two in a row not significant, five in a row is.
Similarly: Disease with 50% fatality rate. New drug: does it work? If it saves 5 patients in a row, then yes it’s “significant”! (14/45) So, to evaluate evidence statistically, you should: • Gather the facts, i.e. the evidence, i.e. the “data”. (e.g. # times in a row your friend distinguished Coke from Pepsi) • Compute the p-value, i.e. the probability of such a result by chance alone – often by multiplying (if independent). • Conclude “significance” if the p-value is very small (e.g. < 5%).
This approach is used in medical studies, scientific experiments, psychology studies, sociology, economics, . . . indeed throughout science and social science. It often works very well.
So, what could possibly go wrong? Lots of things! As we will see . . .
Statistical Evaluation of Evidence – Summary
(15/45) • Gather the facts, i.e. the evidence, i.e. the “data”. (e.g. # times in a row your friend distinguished Coke from Pepsi) • Compute the p-value, i.e. the probability of such a result by chance alone – often by multiplying (if independent). • Conclude “significance” if the p-value is very small (e.g. < 5%).
This approach is used in medical studies, scientific experiments, psychology studies, sociology, economics, . . . indeed throughout science and social science. It often works very well.
So, what could possibly go wrong? Lots of things! As we will see . . .
Statistical Evaluation of Evidence – Summary
So, to evaluate evidence statistically, you should:
(15/45) i.e. the evidence, i.e. the “data”. (e.g. # times in a row your friend distinguished Coke from Pepsi) • Compute the p-value, i.e. the probability of such a result by chance alone – often by multiplying (if independent). • Conclude “significance” if the p-value is very small (e.g. < 5%).
This approach is used in medical studies, scientific experiments, psychology studies, sociology, economics, . . . indeed throughout science and social science. It often works very well.
So, what could possibly go wrong? Lots of things! As we will see . . .
Statistical Evaluation of Evidence – Summary
So, to evaluate evidence statistically, you should: • Gather the facts,
(15/45) i.e. the “data”. (e.g. # times in a row your friend distinguished Coke from Pepsi) • Compute the p-value, i.e. the probability of such a result by chance alone – often by multiplying (if independent). • Conclude “significance” if the p-value is very small (e.g. < 5%).
This approach is used in medical studies, scientific experiments, psychology studies, sociology, economics, . . . indeed throughout science and social science. It often works very well.
So, what could possibly go wrong? Lots of things! As we will see . . .
Statistical Evaluation of Evidence – Summary
So, to evaluate evidence statistically, you should: • Gather the facts, i.e. the evidence,
(15/45) (e.g. # times in a row your friend distinguished Coke from Pepsi) • Compute the p-value, i.e. the probability of such a result by chance alone – often by multiplying (if independent). • Conclude “significance” if the p-value is very small (e.g. < 5%).
This approach is used in medical studies, scientific experiments, psychology studies, sociology, economics, . . . indeed throughout science and social science. It often works very well.
So, what could possibly go wrong? Lots of things! As we will see . . .
Statistical Evaluation of Evidence – Summary
So, to evaluate evidence statistically, you should: • Gather the facts, i.e. the evidence, i.e. the “data”.
(15/45) • Compute the p-value, i.e. the probability of such a result by chance alone – often by multiplying (if independent). • Conclude “significance” if the p-value is very small (e.g. < 5%).
This approach is used in medical studies, scientific experiments, psychology studies, sociology, economics, . . . indeed throughout science and social science. It often works very well.
So, what could possibly go wrong? Lots of things! As we will see . . .
Statistical Evaluation of Evidence – Summary
So, to evaluate evidence statistically, you should: • Gather the facts, i.e. the evidence, i.e. the “data”. (e.g. # times in a row your friend distinguished Coke from Pepsi)
(15/45) i.e. the probability of such a result by chance alone – often by multiplying (if independent). • Conclude “significance” if the p-value is very small (e.g. < 5%).
This approach is used in medical studies, scientific experiments, psychology studies, sociology, economics, . . . indeed throughout science and social science. It often works very well.
So, what could possibly go wrong? Lots of things! As we will see . . .
Statistical Evaluation of Evidence – Summary
So, to evaluate evidence statistically, you should: • Gather the facts, i.e. the evidence, i.e. the “data”. (e.g. # times in a row your friend distinguished Coke from Pepsi) • Compute the p-value,
(15/45) – often by multiplying (if independent). • Conclude “significance” if the p-value is very small (e.g. < 5%).
This approach is used in medical studies, scientific experiments, psychology studies, sociology, economics, . . . indeed throughout science and social science. It often works very well.
So, what could possibly go wrong? Lots of things! As we will see . . .
Statistical Evaluation of Evidence – Summary
So, to evaluate evidence statistically, you should: • Gather the facts, i.e. the evidence, i.e. the “data”. (e.g. # times in a row your friend distinguished Coke from Pepsi) • Compute the p-value, i.e. the probability of such a result by chance alone
(15/45) • Conclude “significance” if the p-value is very small (e.g. < 5%).
This approach is used in medical studies, scientific experiments, psychology studies, sociology, economics, . . . indeed throughout science and social science. It often works very well.
So, what could possibly go wrong? Lots of things! As we will see . . .
Statistical Evaluation of Evidence – Summary
So, to evaluate evidence statistically, you should: • Gather the facts, i.e. the evidence, i.e. the “data”. (e.g. # times in a row your friend distinguished Coke from Pepsi) • Compute the p-value, i.e. the probability of such a result by chance alone – often by multiplying (if independent).
(15/45) (e.g. < 5%).
This approach is used in medical studies, scientific experiments, psychology studies, sociology, economics, . . . indeed throughout science and social science. It often works very well.
So, what could possibly go wrong? Lots of things! As we will see . . .
Statistical Evaluation of Evidence – Summary
So, to evaluate evidence statistically, you should: • Gather the facts, i.e. the evidence, i.e. the “data”. (e.g. # times in a row your friend distinguished Coke from Pepsi) • Compute the p-value, i.e. the probability of such a result by chance alone – often by multiplying (if independent). • Conclude “significance” if the p-value is very small
(15/45) This approach is used in medical studies, scientific experiments, psychology studies, sociology, economics, . . . indeed throughout science and social science. It often works very well.
So, what could possibly go wrong? Lots of things! As we will see . . .
Statistical Evaluation of Evidence – Summary
So, to evaluate evidence statistically, you should: • Gather the facts, i.e. the evidence, i.e. the “data”. (e.g. # times in a row your friend distinguished Coke from Pepsi) • Compute the p-value, i.e. the probability of such a result by chance alone – often by multiplying (if independent). • Conclude “significance” if the p-value is very small (e.g. < 5%).
(15/45) indeed throughout science and social science. It often works very well.
So, what could possibly go wrong? Lots of things! As we will see . . .
Statistical Evaluation of Evidence – Summary
So, to evaluate evidence statistically, you should: • Gather the facts, i.e. the evidence, i.e. the “data”. (e.g. # times in a row your friend distinguished Coke from Pepsi) • Compute the p-value, i.e. the probability of such a result by chance alone – often by multiplying (if independent). • Conclude “significance” if the p-value is very small (e.g. < 5%).
This approach is used in medical studies, scientific experiments, psychology studies, sociology, economics, . . .
(15/45) It often works very well.
So, what could possibly go wrong? Lots of things! As we will see . . .
Statistical Evaluation of Evidence – Summary
So, to evaluate evidence statistically, you should: • Gather the facts, i.e. the evidence, i.e. the “data”. (e.g. # times in a row your friend distinguished Coke from Pepsi) • Compute the p-value, i.e. the probability of such a result by chance alone – often by multiplying (if independent). • Conclude “significance” if the p-value is very small (e.g. < 5%).
This approach is used in medical studies, scientific experiments, psychology studies, sociology, economics, . . . indeed throughout science and social science.
(15/45) So, what could possibly go wrong? Lots of things! As we will see . . .
Statistical Evaluation of Evidence – Summary
So, to evaluate evidence statistically, you should: • Gather the facts, i.e. the evidence, i.e. the “data”. (e.g. # times in a row your friend distinguished Coke from Pepsi) • Compute the p-value, i.e. the probability of such a result by chance alone – often by multiplying (if independent). • Conclude “significance” if the p-value is very small (e.g. < 5%).
This approach is used in medical studies, scientific experiments, psychology studies, sociology, economics, . . . indeed throughout science and social science. It often works very well.
(15/45) Lots of things! As we will see . . .
Statistical Evaluation of Evidence – Summary
So, to evaluate evidence statistically, you should: • Gather the facts, i.e. the evidence, i.e. the “data”. (e.g. # times in a row your friend distinguished Coke from Pepsi) • Compute the p-value, i.e. the probability of such a result by chance alone – often by multiplying (if independent). • Conclude “significance” if the p-value is very small (e.g. < 5%).
This approach is used in medical studies, scientific experiments, psychology studies, sociology, economics, . . . indeed throughout science and social science. It often works very well.
So, what could possibly go wrong?
(15/45) As we will see . . .
Statistical Evaluation of Evidence – Summary
So, to evaluate evidence statistically, you should: • Gather the facts, i.e. the evidence, i.e. the “data”. (e.g. # times in a row your friend distinguished Coke from Pepsi) • Compute the p-value, i.e. the probability of such a result by chance alone – often by multiplying (if independent). • Conclude “significance” if the p-value is very small (e.g. < 5%).
This approach is used in medical studies, scientific experiments, psychology studies, sociology, economics, . . . indeed throughout science and social science. It often works very well.
So, what could possibly go wrong? Lots of things!
(15/45) Statistical Evaluation of Evidence – Summary
So, to evaluate evidence statistically, you should: • Gather the facts, i.e. the evidence, i.e. the “data”. (e.g. # times in a row your friend distinguished Coke from Pepsi) • Compute the p-value, i.e. the probability of such a result by chance alone – often by multiplying (if independent). • Conclude “significance” if the p-value is very small (e.g. < 5%).
This approach is used in medical studies, scientific experiments, psychology studies, sociology, economics, . . . indeed throughout science and social science. It often works very well.
So, what could possibly go wrong? Lots of things! As we will see . . .
(15/45) The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
(16/45) Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear.
(16/45) How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”.
(16/45) (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know?
(16/45) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”)
(16/45) (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians.
(16/45) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”)
(16/45) Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”.
(16/45) Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%.
(16/45) “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media:
(16/45) “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”;
(16/45) “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”;
(16/45) “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”;
(16/45) Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”.
(16/45) Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts:
(16/45) Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005:
(16/45) Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95,
(16/45) Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73,
(16/45) Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99,
(16/45) Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26,
(16/45) So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06.
(16/45) (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe?
(16/45) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”)
(16/45) Toronto 2006: rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias!
(16/45) rate down again (1.86); “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: (16/45) “regained its innocence”??
Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); (16/45) Just the Facts?
The actual facts are often not what they appear. Example: “80% of bar fights involving fatalities were started by the victim”. How do they know? (“sampling bias”) Example: Interviews with successful musicians. (“reporting bias”) Example: Toronto 2005 “Summer of the gun”. Homicides up 22%. Media: “guns used to bathe Toronto in blood”; “Toronto has lost its innocence”; “Gun-crazed gangsters terrorise at will”; “people were tripping over police tape and bullet-riddled bodies on their way to work”. Facts: Homicide rate per 100,000 people, 2005: Toronto CMA 1.95, Winnipeg 3.73, Regina 3.99, Edmonton 4.26, Canada 2.06. So why did people think Toronto was so unsafe? (“headline bias”) So, first, get the facts right, without bias! Toronto 2006: rate down again (1.86); “regained its innocence”?? (16/45) Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not. But why not? The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities:
(17/45) Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not. But why not? The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
(17/45) Cheater? Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not. But why not? The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot.
(17/45) Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not. But why not? The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater?
(17/45) Probability of winning jackpot = one in 14 million (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not. But why not? The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
(17/45) one in 14 million (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not. But why not? The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
Probability of winning jackpot =
(17/45) (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not. But why not? The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million
(17/45) So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not. But why not? The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million (13,983,816).
(17/45) If so, does this mean that John Smith cheated??
No, of course not. But why not? The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million (13,983,816).
So, is the p-value one in 14 million?
(17/45) No, of course not. But why not? The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
(17/45) But why not? The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not.
(17/45) The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not. But why not?
(17/45) We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not. But why not? The “out of how many” principle:
(17/45) In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not. But why not? The “out of how many” principle: We should compute the probability of some such event occurring.
(17/45) out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not. But why not? The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot,
(17/45) Not surprising at all. The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not. But why not? The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket.
(17/45) The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not. But why not? The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all.
(17/45) (Subtle!) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not. But why not? The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small.
(17/45) So, no suspicion of fraud/cheating.
Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not. But why not? The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small. (Subtle!)
(17/45) Interpreting Probabilities: Out of How Many?
Suppose you read that John Smith of Orillia won the Lotto 6/49 lottery jackpot. Cheater? Let’s do some statistical analysis!
Probability of winning jackpot = one in 14 million (13,983,816).
So, is the p-value one in 14 million? If so, does this mean that John Smith cheated??
No, of course not. But why not? The “out of how many” principle: We should compute the probability of some such event occurring. In this case, one person won the jackpot, out of millions of people who bought a ticket. Not surprising at all. The “real” p-value is not small. (Subtle!) So, no suspicion of fraud/cheating. (17/45) True story: Ran into my father’s cousin at Disney World!
Surprise! One chance in 230,000,000? Proves something? But wait. We saw several thousand people there. And, we would have been surprised by hundreds of people. It follows that some such meeting had about one chance in 200. Might well happen over a lifetime. (Has it to you?)
Out of How Many: Example
(18/45) Ran into my father’s cousin at Disney World!
Surprise! One chance in 230,000,000? Proves something? But wait. We saw several thousand people there. And, we would have been surprised by hundreds of people. It follows that some such meeting had about one chance in 200. Might well happen over a lifetime. (Has it to you?)
Out of How Many: Example
True story:
(18/45) Surprise! One chance in 230,000,000? Proves something? But wait. We saw several thousand people there. And, we would have been surprised by hundreds of people. It follows that some such meeting had about one chance in 200. Might well happen over a lifetime. (Has it to you?)
Out of How Many: Example
True story: Ran into my father’s cousin at Disney World!
(18/45) One chance in 230,000,000? Proves something? But wait. We saw several thousand people there. And, we would have been surprised by hundreds of people. It follows that some such meeting had about one chance in 200. Might well happen over a lifetime. (Has it to you?)
Out of How Many: Example
True story: Ran into my father’s cousin at Disney World!
Surprise!
(18/45) Proves something? But wait. We saw several thousand people there. And, we would have been surprised by hundreds of people. It follows that some such meeting had about one chance in 200. Might well happen over a lifetime. (Has it to you?)
Out of How Many: Example
True story: Ran into my father’s cousin at Disney World!
Surprise! One chance in 230,000,000?
(18/45) But wait. We saw several thousand people there. And, we would have been surprised by hundreds of people. It follows that some such meeting had about one chance in 200. Might well happen over a lifetime. (Has it to you?)
Out of How Many: Example
True story: Ran into my father’s cousin at Disney World!
Surprise! One chance in 230,000,000? Proves something?
(18/45) We saw several thousand people there. And, we would have been surprised by hundreds of people. It follows that some such meeting had about one chance in 200. Might well happen over a lifetime. (Has it to you?)
Out of How Many: Example
True story: Ran into my father’s cousin at Disney World!
Surprise! One chance in 230,000,000? Proves something? But wait.
(18/45) And, we would have been surprised by hundreds of people. It follows that some such meeting had about one chance in 200. Might well happen over a lifetime. (Has it to you?)
Out of How Many: Example
True story: Ran into my father’s cousin at Disney World!
Surprise! One chance in 230,000,000? Proves something? But wait. We saw several thousand people there.
(18/45) It follows that some such meeting had about one chance in 200. Might well happen over a lifetime. (Has it to you?)
Out of How Many: Example
True story: Ran into my father’s cousin at Disney World!
Surprise! One chance in 230,000,000? Proves something? But wait. We saw several thousand people there. And, we would have been surprised by hundreds of people.
(18/45) Might well happen over a lifetime. (Has it to you?)
Out of How Many: Example
True story: Ran into my father’s cousin at Disney World!
Surprise! One chance in 230,000,000? Proves something? But wait. We saw several thousand people there. And, we would have been surprised by hundreds of people. It follows that some such meeting had about one chance in 200.
(18/45) (Has it to you?)
Out of How Many: Example
True story: Ran into my father’s cousin at Disney World!
Surprise! One chance in 230,000,000? Proves something? But wait. We saw several thousand people there. And, we would have been surprised by hundreds of people. It follows that some such meeting had about one chance in 200. Might well happen over a lifetime. (18/45) Out of How Many: Example
True story: Ran into my father’s cousin at Disney World!
Surprise! One chance in 230,000,000? Proves something? But wait. We saw several thousand people there. And, we would have been surprised by hundreds of people. It follows that some such meeting had about one chance in 200. Might well happen over a lifetime. (Has it to you?) (18/45) Striking? Yes. Deeper “meaning”? No, just chance! Out of how many other estranged Americans? One success out of a million is luck, not “meaning”.
TV Interview: Reunited Half-Brothers
(19/45) Yes. Deeper “meaning”? No, just chance! Out of how many other estranged Americans? One success out of a million is luck, not “meaning”.
TV Interview: Reunited Half-Brothers
Striking?
(19/45) Deeper “meaning”? No, just chance! Out of how many other estranged Americans? One success out of a million is luck, not “meaning”.
TV Interview: Reunited Half-Brothers
Striking? Yes.
(19/45) No, just chance! Out of how many other estranged Americans? One success out of a million is luck, not “meaning”.
TV Interview: Reunited Half-Brothers
Striking? Yes. Deeper “meaning”?
(19/45) Out of how many other estranged Americans? One success out of a million is luck, not “meaning”.
TV Interview: Reunited Half-Brothers
Striking? Yes. Deeper “meaning”? No, just chance!
(19/45) One success out of a million is luck, not “meaning”.
TV Interview: Reunited Half-Brothers
Striking? Yes. Deeper “meaning”? No, just chance! Out of how many other estranged Americans?
(19/45) TV Interview: Reunited Half-Brothers
Striking? Yes. Deeper “meaning”? No, just chance! Out of how many other estranged Americans? One success out of a million is luck, not “meaning”. (19/45) • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed! Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark
(20/45) • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed! Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England.
(20/45) • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed! Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy.
(20/45) Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed! Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)?
(20/45) • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed! Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?!
(20/45) “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed! Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow:
(20/45) • Convicted! Jailed! Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”.
(20/45) Jailed! Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted!
(20/45) Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed!
(20/45) Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed! Vilified!
(20/45) Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed! Vilified! Later, third son taken away from her (temporarily)!
(20/45) Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed! Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly?
(20/45) Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed! Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute?
(20/45) How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed! Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
(20/45) He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed! Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”?
(20/45) so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed! Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543,
(20/45) (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed! Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply:
(20/45) = 1/72, 982, 849 ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed! Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) (20/45) ≈ 1/73, 000, 000.
Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed! Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 (20/45) Legal Case: Sally Clark • Solicitor in Cheshire, England. • Had two sons; each died in infancy. • “cot death” (SIDS)? Or murder!?! • 1999 testimony by paediatrician Sir Roy Meadow: “the odds against two cot deaths in the same family are 73 million to one”. • Convicted! Jailed! Vilified! Later, third son taken away from her (temporarily)!
Was “73 million to one” computed correctly? Was it the right thing to compute? Perhaps not!
How did Meadow compute that “73 million to one”? He said the probability of one child dying of SIDS was one in 8,543, so for two children dying, we multiply: (1/8, 543) × (1/8, 543) = 1/72, 982, 849 ≈ 1/73, 000, 000. (20/45) Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation?
(21/45) No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid?
(21/45) SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No!
(21/45) so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families,
(21/45) the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case,
(21/45) Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely.
(21/45) No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid?
(21/45) The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No!
(21/45) Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303.
(21/45) (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability
(21/45) But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26).
(21/45) (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability
(21/45) Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls).
(21/45) No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid?
(21/45) Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No!
(21/45) that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family,
(21/45) What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence.
(21/45) (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”?
(21/45) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!)
(21/45) conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”:
(21/45) Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities.
(21/45) “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society:
(21/45) What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid”
(21/45) given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides,
(21/45) Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. (21/45) (Bayesian?) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (21/45) Estimated as perhaps just 1/3.
Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) (21/45) Clark Case: Valid Probability Calculation? Was the multiplication valid? No! SIDS tends to run in families, so once a family has had one SIDS case, the second one is more likely. Was the figure 1/8,543 valid? No! The overall probability of SIDS in the U.K. was 1/1,303. Meadow got 1/8,543 by “adjusting” for family circumstances that lower the SIDS probability (no smokers, someone employed, mother over 26). But neglected other factors which raise the probability (e.g. boys twice as likely as girls). Was the interpretation valid? No! Even if “one in 73 million” is the correct probability of two SIDS cases in this specific family, that’s still not the same as the probability of Clark’s innocence. What about “out of how many”? (Millions of families in the U.K.!) “Prosecutor’s Fallacy”: conflating two different probabilities. Royal Statistical Society: “approach is . . . statistically invalid” What’s really needed is the probability of two infanticides, given either two SIDS deaths or two infanticides. Different (and subtle) question! (Bayesian?) Estimated as perhaps just 1/3. (21/45) • Sally Clark was eventually acquitted, on second appeal, after more than three years in jail. But she never recovered psychologically, and died of alcohol poisoning four years later. • The U.K. General Medical Council ruled that Meadow’s evidence was “misleading and incorrect”, and that he was guilty of “serious professional misconduct”. He was effectively barred from any future court work. • The prosecution pathologist Alan Williams was found to have not reported evidence about an infection in the second son (which suggested death by natural causes). The GMC found him, too, guilty of serious professional misconduct.
• Several other people’s convictions were overturned on appeal.
• Prosecutors/judges everywhere learned a valuable lesson. (?)
Clark Case: Aftermath
(22/45) on second appeal, after more than three years in jail. But she never recovered psychologically, and died of alcohol poisoning four years later. • The U.K. General Medical Council ruled that Meadow’s evidence was “misleading and incorrect”, and that he was guilty of “serious professional misconduct”. He was effectively barred from any future court work. • The prosecution pathologist Alan Williams was found to have not reported evidence about an infection in the second son (which suggested death by natural causes). The GMC found him, too, guilty of serious professional misconduct.
• Several other people’s convictions were overturned on appeal.
• Prosecutors/judges everywhere learned a valuable lesson. (?)
Clark Case: Aftermath
• Sally Clark was eventually acquitted,
(22/45) after more than three years in jail. But she never recovered psychologically, and died of alcohol poisoning four years later. • The U.K. General Medical Council ruled that Meadow’s evidence was “misleading and incorrect”, and that he was guilty of “serious professional misconduct”. He was effectively barred from any future court work. • The prosecution pathologist Alan Williams was found to have not reported evidence about an infection in the second son (which suggested death by natural causes). The GMC found him, too, guilty of serious professional misconduct.
• Several other people’s convictions were overturned on appeal.
• Prosecutors/judges everywhere learned a valuable lesson. (?)
Clark Case: Aftermath
• Sally Clark was eventually acquitted, on second appeal,
(22/45) But she never recovered psychologically, and died of alcohol poisoning four years later. • The U.K. General Medical Council ruled that Meadow’s evidence was “misleading and incorrect”, and that he was guilty of “serious professional misconduct”. He was effectively barred from any future court work. • The prosecution pathologist Alan Williams was found to have not reported evidence about an infection in the second son (which suggested death by natural causes). The GMC found him, too, guilty of serious professional misconduct.
• Several other people’s convictions were overturned on appeal.
• Prosecutors/judges everywhere learned a valuable lesson. (?)
Clark Case: Aftermath
• Sally Clark was eventually acquitted, on second appeal, after more than three years in jail.
(22/45) and died of alcohol poisoning four years later. • The U.K. General Medical Council ruled that Meadow’s evidence was “misleading and incorrect”, and that he was guilty of “serious professional misconduct”. He was effectively barred from any future court work. • The prosecution pathologist Alan Williams was found to have not reported evidence about an infection in the second son (which suggested death by natural causes). The GMC found him, too, guilty of serious professional misconduct.
• Several other people’s convictions were overturned on appeal.
• Prosecutors/judges everywhere learned a valuable lesson. (?)
Clark Case: Aftermath
• Sally Clark was eventually acquitted, on second appeal, after more than three years in jail. But she never recovered psychologically,
(22/45) • The U.K. General Medical Council ruled that Meadow’s evidence was “misleading and incorrect”, and that he was guilty of “serious professional misconduct”. He was effectively barred from any future court work. • The prosecution pathologist Alan Williams was found to have not reported evidence about an infection in the second son (which suggested death by natural causes). The GMC found him, too, guilty of serious professional misconduct.
• Several other people’s convictions were overturned on appeal.
• Prosecutors/judges everywhere learned a valuable lesson. (?)
Clark Case: Aftermath
• Sally Clark was eventually acquitted, on second appeal, after more than three years in jail. But she never recovered psychologically, and died of alcohol poisoning four years later.
(22/45) and that he was guilty of “serious professional misconduct”. He was effectively barred from any future court work. • The prosecution pathologist Alan Williams was found to have not reported evidence about an infection in the second son (which suggested death by natural causes). The GMC found him, too, guilty of serious professional misconduct.
• Several other people’s convictions were overturned on appeal.
• Prosecutors/judges everywhere learned a valuable lesson. (?)
Clark Case: Aftermath
• Sally Clark was eventually acquitted, on second appeal, after more than three years in jail. But she never recovered psychologically, and died of alcohol poisoning four years later. • The U.K. General Medical Council ruled that Meadow’s evidence was “misleading and incorrect”,
(22/45) He was effectively barred from any future court work. • The prosecution pathologist Alan Williams was found to have not reported evidence about an infection in the second son (which suggested death by natural causes). The GMC found him, too, guilty of serious professional misconduct.
• Several other people’s convictions were overturned on appeal.
• Prosecutors/judges everywhere learned a valuable lesson. (?)
Clark Case: Aftermath
• Sally Clark was eventually acquitted, on second appeal, after more than three years in jail. But she never recovered psychologically, and died of alcohol poisoning four years later. • The U.K. General Medical Council ruled that Meadow’s evidence was “misleading and incorrect”, and that he was guilty of “serious professional misconduct”.
(22/45) • The prosecution pathologist Alan Williams was found to have not reported evidence about an infection in the second son (which suggested death by natural causes). The GMC found him, too, guilty of serious professional misconduct.
• Several other people’s convictions were overturned on appeal.
• Prosecutors/judges everywhere learned a valuable lesson. (?)
Clark Case: Aftermath
• Sally Clark was eventually acquitted, on second appeal, after more than three years in jail. But she never recovered psychologically, and died of alcohol poisoning four years later. • The U.K. General Medical Council ruled that Meadow’s evidence was “misleading and incorrect”, and that he was guilty of “serious professional misconduct”. He was effectively barred from any future court work.
(22/45) The GMC found him, too, guilty of serious professional misconduct.
• Several other people’s convictions were overturned on appeal.
• Prosecutors/judges everywhere learned a valuable lesson. (?)
Clark Case: Aftermath
• Sally Clark was eventually acquitted, on second appeal, after more than three years in jail. But she never recovered psychologically, and died of alcohol poisoning four years later. • The U.K. General Medical Council ruled that Meadow’s evidence was “misleading and incorrect”, and that he was guilty of “serious professional misconduct”. He was effectively barred from any future court work. • The prosecution pathologist Alan Williams was found to have not reported evidence about an infection in the second son (which suggested death by natural causes).
(22/45) • Several other people’s convictions were overturned on appeal.
• Prosecutors/judges everywhere learned a valuable lesson. (?)
Clark Case: Aftermath
• Sally Clark was eventually acquitted, on second appeal, after more than three years in jail. But she never recovered psychologically, and died of alcohol poisoning four years later. • The U.K. General Medical Council ruled that Meadow’s evidence was “misleading and incorrect”, and that he was guilty of “serious professional misconduct”. He was effectively barred from any future court work. • The prosecution pathologist Alan Williams was found to have not reported evidence about an infection in the second son (which suggested death by natural causes). The GMC found him, too, guilty of serious professional misconduct.
(22/45) • Prosecutors/judges everywhere learned a valuable lesson. (?)
Clark Case: Aftermath
• Sally Clark was eventually acquitted, on second appeal, after more than three years in jail. But she never recovered psychologically, and died of alcohol poisoning four years later. • The U.K. General Medical Council ruled that Meadow’s evidence was “misleading and incorrect”, and that he was guilty of “serious professional misconduct”. He was effectively barred from any future court work. • The prosecution pathologist Alan Williams was found to have not reported evidence about an infection in the second son (which suggested death by natural causes). The GMC found him, too, guilty of serious professional misconduct.
• Several other people’s convictions were overturned on appeal.
(22/45) (?)
Clark Case: Aftermath
• Sally Clark was eventually acquitted, on second appeal, after more than three years in jail. But she never recovered psychologically, and died of alcohol poisoning four years later. • The U.K. General Medical Council ruled that Meadow’s evidence was “misleading and incorrect”, and that he was guilty of “serious professional misconduct”. He was effectively barred from any future court work. • The prosecution pathologist Alan Williams was found to have not reported evidence about an infection in the second son (which suggested death by natural causes). The GMC found him, too, guilty of serious professional misconduct.
• Several other people’s convictions were overturned on appeal.
• Prosecutors/judges everywhere learned a valuable lesson.
(22/45) Clark Case: Aftermath
• Sally Clark was eventually acquitted, on second appeal, after more than three years in jail. But she never recovered psychologically, and died of alcohol poisoning four years later. • The U.K. General Medical Council ruled that Meadow’s evidence was “misleading and incorrect”, and that he was guilty of “serious professional misconduct”. He was effectively barred from any future court work. • The prosecution pathologist Alan Williams was found to have not reported evidence about an infection in the second son (which suggested death by natural causes). The GMC found him, too, guilty of serious professional misconduct.
• Several other people’s convictions were overturned on appeal.
• Prosecutors/judges everywhere learned a valuable lesson. (?)
(22/45) • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins
(23/45) an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles,
(23/45) and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley,
(23/45) • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen.
(23/45) a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said:
(23/45) with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman
(23/45) ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail
(23/45) into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse
(23/45) which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car
(23/45) who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man
(23/45) • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache.
(23/45) because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested,
(23/45) (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics
(23/45) • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly).
(23/45) The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”.
(23/45) – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities:
(23/45) – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10
(23/45) – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4
(23/45) – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3
(23/45) – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10
(23/45) – Yellow car : 1 out of 10
An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000
(23/45) An Earlier Similar Case: Malcolm Collins • On June 18, 1964, in Los Angeles, an elderly lady was pushed down in an alley, and her purse was stolen. • Witnesses said: a young Caucasian woman with a dark blond ponytail ran away with the purse into a yellow car which was driven by a Black man who had a beard and moustache. • Four days later, Malcolm and Janet Collins were arrested, because they fit these characteristics (mostly). • At trial, the prosecutor called “a mathematics instructor at a nearby state college”. The prosecutor told the mathematician to assume certain (“conservative”?) probabilities: – Black man with a beard: 1 out of 10 – Man with moustache: 1 out of 4 – White woman with blonde hair: 1 out of 3 – Woman with a ponytail: 1 out of 10 – Interracial couple in car: 1 out of 1,000 – Yellow car : 1 out of 10 (23/45) by multiplying: (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10) = 1/12, 000, 000 Was this reasoning valid? • The facts? No, these individual probabilities were just assumed. • Multiplying? No way! e.g. if have a beard then likely also have a moustache! Similarly, if have Black man and White woman, then of course have an Interracial couple! The calculation was extremely faulty! • Correctly interpreted probability? No! Remember “out of how many”! Los Angeles County population in 1964: 6,537,000. So, the probability of two such couples is quite large! And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics – a different and subtle question with a much smaller answer.
The mathematician then computed the probability that a random couple would satisfy all of these criteria,
(24/45) (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10) = 1/12, 000, 000 Was this reasoning valid? • The facts? No, these individual probabilities were just assumed. • Multiplying? No way! e.g. if have a beard then likely also have a moustache! Similarly, if have Black man and White woman, then of course have an Interracial couple! The calculation was extremely faulty! • Correctly interpreted probability? No! Remember “out of how many”! Los Angeles County population in 1964: 6,537,000. So, the probability of two such couples is quite large! And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics – a different and subtle question with a much smaller answer.
The mathematician then computed the probability that a random couple would satisfy all of these criteria, by multiplying:
(24/45) = 1/12, 000, 000 Was this reasoning valid? • The facts? No, these individual probabilities were just assumed. • Multiplying? No way! e.g. if have a beard then likely also have a moustache! Similarly, if have Black man and White woman, then of course have an Interracial couple! The calculation was extremely faulty! • Correctly interpreted probability? No! Remember “out of how many”! Los Angeles County population in 1964: 6,537,000. So, the probability of two such couples is quite large! And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics – a different and subtle question with a much smaller answer.
The mathematician then computed the probability that a random couple would satisfy all of these criteria, by multiplying: (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10)
(24/45) Was this reasoning valid? • The facts? No, these individual probabilities were just assumed. • Multiplying? No way! e.g. if have a beard then likely also have a moustache! Similarly, if have Black man and White woman, then of course have an Interracial couple! The calculation was extremely faulty! • Correctly interpreted probability? No! Remember “out of how many”! Los Angeles County population in 1964: 6,537,000. So, the probability of two such couples is quite large! And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics – a different and subtle question with a much smaller answer.
The mathematician then computed the probability that a random couple would satisfy all of these criteria, by multiplying: (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10) = 1/12, 000, 000
(24/45) • The facts? No, these individual probabilities were just assumed. • Multiplying? No way! e.g. if have a beard then likely also have a moustache! Similarly, if have Black man and White woman, then of course have an Interracial couple! The calculation was extremely faulty! • Correctly interpreted probability? No! Remember “out of how many”! Los Angeles County population in 1964: 6,537,000. So, the probability of two such couples is quite large! And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics – a different and subtle question with a much smaller answer.
The mathematician then computed the probability that a random couple would satisfy all of these criteria, by multiplying: (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10) = 1/12, 000, 000 Was this reasoning valid?
(24/45) No, these individual probabilities were just assumed. • Multiplying? No way! e.g. if have a beard then likely also have a moustache! Similarly, if have Black man and White woman, then of course have an Interracial couple! The calculation was extremely faulty! • Correctly interpreted probability? No! Remember “out of how many”! Los Angeles County population in 1964: 6,537,000. So, the probability of two such couples is quite large! And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics – a different and subtle question with a much smaller answer.
The mathematician then computed the probability that a random couple would satisfy all of these criteria, by multiplying: (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10) = 1/12, 000, 000 Was this reasoning valid? • The facts?
(24/45) • Multiplying? No way! e.g. if have a beard then likely also have a moustache! Similarly, if have Black man and White woman, then of course have an Interracial couple! The calculation was extremely faulty! • Correctly interpreted probability? No! Remember “out of how many”! Los Angeles County population in 1964: 6,537,000. So, the probability of two such couples is quite large! And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics – a different and subtle question with a much smaller answer.
The mathematician then computed the probability that a random couple would satisfy all of these criteria, by multiplying: (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10) = 1/12, 000, 000 Was this reasoning valid? • The facts? No, these individual probabilities were just assumed.
(24/45) Similarly, if have Black man and White woman, then of course have an Interracial couple! The calculation was extremely faulty! • Correctly interpreted probability? No! Remember “out of how many”! Los Angeles County population in 1964: 6,537,000. So, the probability of two such couples is quite large! And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics – a different and subtle question with a much smaller answer.
The mathematician then computed the probability that a random couple would satisfy all of these criteria, by multiplying: (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10) = 1/12, 000, 000 Was this reasoning valid? • The facts? No, these individual probabilities were just assumed. • Multiplying? No way! e.g. if have a beard then likely also have a moustache!
(24/45) The calculation was extremely faulty! • Correctly interpreted probability? No! Remember “out of how many”! Los Angeles County population in 1964: 6,537,000. So, the probability of two such couples is quite large! And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics – a different and subtle question with a much smaller answer.
The mathematician then computed the probability that a random couple would satisfy all of these criteria, by multiplying: (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10) = 1/12, 000, 000 Was this reasoning valid? • The facts? No, these individual probabilities were just assumed. • Multiplying? No way! e.g. if have a beard then likely also have a moustache! Similarly, if have Black man and White woman, then of course have an Interracial couple!
(24/45) • Correctly interpreted probability? No! Remember “out of how many”! Los Angeles County population in 1964: 6,537,000. So, the probability of two such couples is quite large! And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics – a different and subtle question with a much smaller answer.
The mathematician then computed the probability that a random couple would satisfy all of these criteria, by multiplying: (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10) = 1/12, 000, 000 Was this reasoning valid? • The facts? No, these individual probabilities were just assumed. • Multiplying? No way! e.g. if have a beard then likely also have a moustache! Similarly, if have Black man and White woman, then of course have an Interracial couple! The calculation was extremely faulty!
(24/45) No! Remember “out of how many”! Los Angeles County population in 1964: 6,537,000. So, the probability of two such couples is quite large! And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics – a different and subtle question with a much smaller answer.
The mathematician then computed the probability that a random couple would satisfy all of these criteria, by multiplying: (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10) = 1/12, 000, 000 Was this reasoning valid? • The facts? No, these individual probabilities were just assumed. • Multiplying? No way! e.g. if have a beard then likely also have a moustache! Similarly, if have Black man and White woman, then of course have an Interracial couple! The calculation was extremely faulty! • Correctly interpreted probability?
(24/45) Remember “out of how many”! Los Angeles County population in 1964: 6,537,000. So, the probability of two such couples is quite large! And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics – a different and subtle question with a much smaller answer.
The mathematician then computed the probability that a random couple would satisfy all of these criteria, by multiplying: (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10) = 1/12, 000, 000 Was this reasoning valid? • The facts? No, these individual probabilities were just assumed. • Multiplying? No way! e.g. if have a beard then likely also have a moustache! Similarly, if have Black man and White woman, then of course have an Interracial couple! The calculation was extremely faulty! • Correctly interpreted probability? No!
(24/45) Los Angeles County population in 1964: 6,537,000. So, the probability of two such couples is quite large! And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics – a different and subtle question with a much smaller answer.
The mathematician then computed the probability that a random couple would satisfy all of these criteria, by multiplying: (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10) = 1/12, 000, 000 Was this reasoning valid? • The facts? No, these individual probabilities were just assumed. • Multiplying? No way! e.g. if have a beard then likely also have a moustache! Similarly, if have Black man and White woman, then of course have an Interracial couple! The calculation was extremely faulty! • Correctly interpreted probability? No! Remember “out of how many”!
(24/45) 6,537,000. So, the probability of two such couples is quite large! And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics – a different and subtle question with a much smaller answer.
The mathematician then computed the probability that a random couple would satisfy all of these criteria, by multiplying: (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10) = 1/12, 000, 000 Was this reasoning valid? • The facts? No, these individual probabilities were just assumed. • Multiplying? No way! e.g. if have a beard then likely also have a moustache! Similarly, if have Black man and White woman, then of course have an Interracial couple! The calculation was extremely faulty! • Correctly interpreted probability? No! Remember “out of how many”! Los Angeles County population in 1964:
(24/45) So, the probability of two such couples is quite large! And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics – a different and subtle question with a much smaller answer.
The mathematician then computed the probability that a random couple would satisfy all of these criteria, by multiplying: (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10) = 1/12, 000, 000 Was this reasoning valid? • The facts? No, these individual probabilities were just assumed. • Multiplying? No way! e.g. if have a beard then likely also have a moustache! Similarly, if have Black man and White woman, then of course have an Interracial couple! The calculation was extremely faulty! • Correctly interpreted probability? No! Remember “out of how many”! Los Angeles County population in 1964: 6,537,000.
(24/45) And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics – a different and subtle question with a much smaller answer.
The mathematician then computed the probability that a random couple would satisfy all of these criteria, by multiplying: (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10) = 1/12, 000, 000 Was this reasoning valid? • The facts? No, these individual probabilities were just assumed. • Multiplying? No way! e.g. if have a beard then likely also have a moustache! Similarly, if have Black man and White woman, then of course have an Interracial couple! The calculation was extremely faulty! • Correctly interpreted probability? No! Remember “out of how many”! Los Angeles County population in 1964: 6,537,000. So, the probability of two such couples is quite large!
(24/45) – a different and subtle question with a much smaller answer.
The mathematician then computed the probability that a random couple would satisfy all of these criteria, by multiplying: (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10) = 1/12, 000, 000 Was this reasoning valid? • The facts? No, these individual probabilities were just assumed. • Multiplying? No way! e.g. if have a beard then likely also have a moustache! Similarly, if have Black man and White woman, then of course have an Interracial couple! The calculation was extremely faulty! • Correctly interpreted probability? No! Remember “out of how many”! Los Angeles County population in 1964: 6,537,000. So, the probability of two such couples is quite large! And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics
(24/45) The mathematician then computed the probability that a random couple would satisfy all of these criteria, by multiplying: (1/10)×(1/4)×(1/3)×(1/10)×(1/1000)×(1/10) = 1/12, 000, 000 Was this reasoning valid? • The facts? No, these individual probabilities were just assumed. • Multiplying? No way! e.g. if have a beard then likely also have a moustache! Similarly, if have Black man and White woman, then of course have an Interracial couple! The calculation was extremely faulty! • Correctly interpreted probability? No! Remember “out of how many”! Los Angeles County population in 1964: 6,537,000. So, the probability of two such couples is quite large! And again, what’s really needed is the probability of Collins being guilty given all of the above characteristics – a different and subtle question with a much smaller answer. (24/45) • Supreme Court of California appeal, March 11, 1968: “We deal here with the novel question whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case. While we discern no inherent incompatibility between the disciplines of law and mathematics and intend no general disapproval or disparagement of the latter as an auxiliary in the fact-finding processes of the former, we cannot uphold the technique employed in the instant case. As we explain in detail, infra, the testimony as to mathematical probability infected the case with fatal error and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules. Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him. We conclude that on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial. We reverse the judgment.”
• Collins was convicted at trial, based on this 1/12M probability.
(25/45) “We deal here with the novel question whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case. While we discern no inherent incompatibility between the disciplines of law and mathematics and intend no general disapproval or disparagement of the latter as an auxiliary in the fact-finding processes of the former, we cannot uphold the technique employed in the instant case. As we explain in detail, infra, the testimony as to mathematical probability infected the case with fatal error and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules. Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him. We conclude that on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial. We reverse the judgment.”
• Collins was convicted at trial, based on this 1/12M probability. • Supreme Court of California appeal, March 11, 1968:
(25/45) While we discern no inherent incompatibility between the disciplines of law and mathematics and intend no general disapproval or disparagement of the latter as an auxiliary in the fact-finding processes of the former, we cannot uphold the technique employed in the instant case. As we explain in detail, infra, the testimony as to mathematical probability infected the case with fatal error and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules. Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him. We conclude that on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial. We reverse the judgment.”
• Collins was convicted at trial, based on this 1/12M probability. • Supreme Court of California appeal, March 11, 1968: “We deal here with the novel question whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case.
(25/45) and intend no general disapproval or disparagement of the latter as an auxiliary in the fact-finding processes of the former, we cannot uphold the technique employed in the instant case. As we explain in detail, infra, the testimony as to mathematical probability infected the case with fatal error and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules. Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him. We conclude that on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial. We reverse the judgment.”
• Collins was convicted at trial, based on this 1/12M probability. • Supreme Court of California appeal, March 11, 1968: “We deal here with the novel question whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case. While we discern no inherent incompatibility between the disciplines of law and mathematics
(25/45) as an auxiliary in the fact-finding processes of the former, we cannot uphold the technique employed in the instant case. As we explain in detail, infra, the testimony as to mathematical probability infected the case with fatal error and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules. Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him. We conclude that on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial. We reverse the judgment.”
• Collins was convicted at trial, based on this 1/12M probability. • Supreme Court of California appeal, March 11, 1968: “We deal here with the novel question whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case. While we discern no inherent incompatibility between the disciplines of law and mathematics and intend no general disapproval or disparagement of the latter
(25/45) we cannot uphold the technique employed in the instant case. As we explain in detail, infra, the testimony as to mathematical probability infected the case with fatal error and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules. Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him. We conclude that on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial. We reverse the judgment.”
• Collins was convicted at trial, based on this 1/12M probability. • Supreme Court of California appeal, March 11, 1968: “We deal here with the novel question whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case. While we discern no inherent incompatibility between the disciplines of law and mathematics and intend no general disapproval or disparagement of the latter as an auxiliary in the fact-finding processes of the former,
(25/45) As we explain in detail, infra, the testimony as to mathematical probability infected the case with fatal error and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules. Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him. We conclude that on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial. We reverse the judgment.”
• Collins was convicted at trial, based on this 1/12M probability. • Supreme Court of California appeal, March 11, 1968: “We deal here with the novel question whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case. While we discern no inherent incompatibility between the disciplines of law and mathematics and intend no general disapproval or disparagement of the latter as an auxiliary in the fact-finding processes of the former, we cannot uphold the technique employed in the instant case.
(25/45) the testimony as to mathematical probability infected the case with fatal error and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules. Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him. We conclude that on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial. We reverse the judgment.”
• Collins was convicted at trial, based on this 1/12M probability. • Supreme Court of California appeal, March 11, 1968: “We deal here with the novel question whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case. While we discern no inherent incompatibility between the disciplines of law and mathematics and intend no general disapproval or disparagement of the latter as an auxiliary in the fact-finding processes of the former, we cannot uphold the technique employed in the instant case. As we explain in detail, infra,
(25/45) and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules. Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him. We conclude that on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial. We reverse the judgment.”
• Collins was convicted at trial, based on this 1/12M probability. • Supreme Court of California appeal, March 11, 1968: “We deal here with the novel question whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case. While we discern no inherent incompatibility between the disciplines of law and mathematics and intend no general disapproval or disparagement of the latter as an auxiliary in the fact-finding processes of the former, we cannot uphold the technique employed in the instant case. As we explain in detail, infra, the testimony as to mathematical probability infected the case with fatal error
(25/45) Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him. We conclude that on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial. We reverse the judgment.”
• Collins was convicted at trial, based on this 1/12M probability. • Supreme Court of California appeal, March 11, 1968: “We deal here with the novel question whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case. While we discern no inherent incompatibility between the disciplines of law and mathematics and intend no general disapproval or disparagement of the latter as an auxiliary in the fact-finding processes of the former, we cannot uphold the technique employed in the instant case. As we explain in detail, infra, the testimony as to mathematical probability infected the case with fatal error and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules.
(25/45) while assisting the trier of fact in the search for truth, must not cast a spell over him. We conclude that on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial. We reverse the judgment.”
• Collins was convicted at trial, based on this 1/12M probability. • Supreme Court of California appeal, March 11, 1968: “We deal here with the novel question whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case. While we discern no inherent incompatibility between the disciplines of law and mathematics and intend no general disapproval or disparagement of the latter as an auxiliary in the fact-finding processes of the former, we cannot uphold the technique employed in the instant case. As we explain in detail, infra, the testimony as to mathematical probability infected the case with fatal error and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules. Mathematics, a veritable sorcerer in our computerized society,
(25/45) must not cast a spell over him. We conclude that on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial. We reverse the judgment.”
• Collins was convicted at trial, based on this 1/12M probability. • Supreme Court of California appeal, March 11, 1968: “We deal here with the novel question whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case. While we discern no inherent incompatibility between the disciplines of law and mathematics and intend no general disapproval or disparagement of the latter as an auxiliary in the fact-finding processes of the former, we cannot uphold the technique employed in the instant case. As we explain in detail, infra, the testimony as to mathematical probability infected the case with fatal error and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules. Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth,
(25/45) We conclude that on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial. We reverse the judgment.”
• Collins was convicted at trial, based on this 1/12M probability. • Supreme Court of California appeal, March 11, 1968: “We deal here with the novel question whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case. While we discern no inherent incompatibility between the disciplines of law and mathematics and intend no general disapproval or disparagement of the latter as an auxiliary in the fact-finding processes of the former, we cannot uphold the technique employed in the instant case. As we explain in detail, infra, the testimony as to mathematical probability infected the case with fatal error and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules. Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him.
(25/45) and that he is entitled to a new trial. We reverse the judgment.”
• Collins was convicted at trial, based on this 1/12M probability. • Supreme Court of California appeal, March 11, 1968: “We deal here with the novel question whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case. While we discern no inherent incompatibility between the disciplines of law and mathematics and intend no general disapproval or disparagement of the latter as an auxiliary in the fact-finding processes of the former, we cannot uphold the technique employed in the instant case. As we explain in detail, infra, the testimony as to mathematical probability infected the case with fatal error and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules. Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him. We conclude that on the record before us defendant should not have had his guilt determined by the odds
(25/45) We reverse the judgment.”
• Collins was convicted at trial, based on this 1/12M probability. • Supreme Court of California appeal, March 11, 1968: “We deal here with the novel question whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case. While we discern no inherent incompatibility between the disciplines of law and mathematics and intend no general disapproval or disparagement of the latter as an auxiliary in the fact-finding processes of the former, we cannot uphold the technique employed in the instant case. As we explain in detail, infra, the testimony as to mathematical probability infected the case with fatal error and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules. Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him. We conclude that on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial. (25/45) • Collins was convicted at trial, based on this 1/12M probability. • Supreme Court of California appeal, March 11, 1968: “We deal here with the novel question whether evidence of mathematical probability has been properly introduced and used by the prosecution in a criminal case. While we discern no inherent incompatibility between the disciplines of law and mathematics and intend no general disapproval or disparagement of the latter as an auxiliary in the fact-finding processes of the former, we cannot uphold the technique employed in the instant case. As we explain in detail, infra, the testimony as to mathematical probability infected the case with fatal error and distorted the jury’s traditional role of determining guilt or innocence according to long-settled rules. Mathematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him. We conclude that on the record before us defendant should not have had his guilt determined by the odds and that he is entitled to a new trial. We reverse the judgment.” (25/45) • Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
(26/45) • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands.
(26/45) after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders,
(26/45) she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards,
(26/45) (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents”
(26/45) • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation).
(26/45) one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003):
(26/45) • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone!
(26/45) Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts?
(26/45) (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts
(26/45) and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after),
(26/45) Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc.
(26/45) etc. • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients,
(26/45) • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc.
(26/45) No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation?
(26/45) Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No!
(26/45) Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No! Out of how many?
(26/45) is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts
(26/45) • Valid calculation? Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”.
(26/45) Many statisticians thought no!
Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? (26/45) Another Case: Lucia de Berk
• Hospital nurse in The Hague, Netherlands. • Arrested for several murders and attempted murders, after discovery that despite working just 203 of the 2,694 shifts in her three wards, she was on duty for 14 of 27 “incidents” (i.e. deaths, or near-deaths requiring reanimation). • Prosecution (2003): one chance in 342 million by chance alone! • Accurate facts? Some controversy whether all these incidents had actually taken place during de Berk’s shifts (not just before or just after), and whether definition of “incident” was adjusted post hoc. Also, she was assigned to many elderly/terminal patients, etc. • Accurate interpretation? No! Out of how many? Once again, the probability that de Berk is guilty given the above facts is quite a different probability from this “one chance in 342 million”. • Valid calculation? Many statisticians thought no! (26/45) • The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
(27/45) had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers,
(27/45) by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”,
(27/45) • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals).
(27/45) Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient?
(27/45) Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not!
(27/45) / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands
(27/45) Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World.
(27/45) • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them?
(27/45) “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that
(27/45) It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”.
(27/45) and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”,
(27/45) • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”!
(27/45) But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable.
(27/45) and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small,
(27/45) • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly.
(27/45) de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist:
(27/45) e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary!
(27/45) de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death,
(27/45) (of reading Tarot cards??)
de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (27/45) de Berk Case: Valid Probability Calculation?
• The prosecution statistician, Henk Elffers, had tried to account for “out of how many”, by multiplying by 27 (the number of nurses in one of the hospitals). • Is that sufficient? Surely not! Many more nurses somewhere in the Netherlands / World. Multiply by all of them? • One statistics paper complained that “the data are used twice: first to identify the suspect, and again in the computation of Elffers’ probabilities”. It made numerous “adjustments”, and eventually reduced “1 in 342 million” to “1 in 45”! • I actually think this paper adjusted too much, and Elffers calculations weren’t so unreasonable. But “1 in 342 million” is surely too small, and was surely not interpreted correctly. • Another twist: de Berk’s diary! e.g. on the day of one (elderly) patient’s death, de Berk wrote that she had “given in to her compulsion.” (of reading Tarot cards??) (27/45) • de Berk was convicted of multiple murders and attempted murders in March 2003, primarily on the basis of “1 in 342 million”. • The convictions were upheld on appeal, June 2004. • However, by the appeal date, enough doubts had been raised about the statistical calculations that the conviction was upheld mostly on other grounds, notably elevated digoxin levels in some of the corpses (evidence of poisoning?). • October 2007 Dutch “Posthumus II Commission” report: “the hypothesis of digoxin poisoning was disproven [through new testing; similar to Susan Nelles case], the statistical data were biased and the analysis incorrect, and the conclusions drawn from it invalid.” • Case reopened June 2008. Not guilty verdict, April 2010. • Of course, she still might be guilty! (Mercy killings?) • But the statistical evidence wasn’t convincing.
de Berk Case: So What Happened?
(28/45) primarily on the basis of “1 in 342 million”. • The convictions were upheld on appeal, June 2004. • However, by the appeal date, enough doubts had been raised about the statistical calculations that the conviction was upheld mostly on other grounds, notably elevated digoxin levels in some of the corpses (evidence of poisoning?). • October 2007 Dutch “Posthumus II Commission” report: “the hypothesis of digoxin poisoning was disproven [through new testing; similar to Susan Nelles case], the statistical data were biased and the analysis incorrect, and the conclusions drawn from it invalid.” • Case reopened June 2008. Not guilty verdict, April 2010. • Of course, she still might be guilty! (Mercy killings?) • But the statistical evidence wasn’t convincing.
de Berk Case: So What Happened?
• de Berk was convicted of multiple murders and attempted murders in March 2003,
(28/45) • The convictions were upheld on appeal, June 2004. • However, by the appeal date, enough doubts had been raised about the statistical calculations that the conviction was upheld mostly on other grounds, notably elevated digoxin levels in some of the corpses (evidence of poisoning?). • October 2007 Dutch “Posthumus II Commission” report: “the hypothesis of digoxin poisoning was disproven [through new testing; similar to Susan Nelles case], the statistical data were biased and the analysis incorrect, and the conclusions drawn from it invalid.” • Case reopened June 2008. Not guilty verdict, April 2010. • Of course, she still might be guilty! (Mercy killings?) • But the statistical evidence wasn’t convincing.
de Berk Case: So What Happened?
• de Berk was convicted of multiple murders and attempted murders in March 2003, primarily on the basis of “1 in 342 million”.
(28/45) • However, by the appeal date, enough doubts had been raised about the statistical calculations that the conviction was upheld mostly on other grounds, notably elevated digoxin levels in some of the corpses (evidence of poisoning?). • October 2007 Dutch “Posthumus II Commission” report: “the hypothesis of digoxin poisoning was disproven [through new testing; similar to Susan Nelles case], the statistical data were biased and the analysis incorrect, and the conclusions drawn from it invalid.” • Case reopened June 2008. Not guilty verdict, April 2010. • Of course, she still might be guilty! (Mercy killings?) • But the statistical evidence wasn’t convincing.
de Berk Case: So What Happened?
• de Berk was convicted of multiple murders and attempted murders in March 2003, primarily on the basis of “1 in 342 million”. • The convictions were upheld on appeal, June 2004.
(28/45) that the conviction was upheld mostly on other grounds, notably elevated digoxin levels in some of the corpses (evidence of poisoning?). • October 2007 Dutch “Posthumus II Commission” report: “the hypothesis of digoxin poisoning was disproven [through new testing; similar to Susan Nelles case], the statistical data were biased and the analysis incorrect, and the conclusions drawn from it invalid.” • Case reopened June 2008. Not guilty verdict, April 2010. • Of course, she still might be guilty! (Mercy killings?) • But the statistical evidence wasn’t convincing.
de Berk Case: So What Happened?
• de Berk was convicted of multiple murders and attempted murders in March 2003, primarily on the basis of “1 in 342 million”. • The convictions were upheld on appeal, June 2004. • However, by the appeal date, enough doubts had been raised about the statistical calculations
(28/45) notably elevated digoxin levels in some of the corpses (evidence of poisoning?). • October 2007 Dutch “Posthumus II Commission” report: “the hypothesis of digoxin poisoning was disproven [through new testing; similar to Susan Nelles case], the statistical data were biased and the analysis incorrect, and the conclusions drawn from it invalid.” • Case reopened June 2008. Not guilty verdict, April 2010. • Of course, she still might be guilty! (Mercy killings?) • But the statistical evidence wasn’t convincing.
de Berk Case: So What Happened?
• de Berk was convicted of multiple murders and attempted murders in March 2003, primarily on the basis of “1 in 342 million”. • The convictions were upheld on appeal, June 2004. • However, by the appeal date, enough doubts had been raised about the statistical calculations that the conviction was upheld mostly on other grounds,
(28/45) • October 2007 Dutch “Posthumus II Commission” report: “the hypothesis of digoxin poisoning was disproven [through new testing; similar to Susan Nelles case], the statistical data were biased and the analysis incorrect, and the conclusions drawn from it invalid.” • Case reopened June 2008. Not guilty verdict, April 2010. • Of course, she still might be guilty! (Mercy killings?) • But the statistical evidence wasn’t convincing.
de Berk Case: So What Happened?
• de Berk was convicted of multiple murders and attempted murders in March 2003, primarily on the basis of “1 in 342 million”. • The convictions were upheld on appeal, June 2004. • However, by the appeal date, enough doubts had been raised about the statistical calculations that the conviction was upheld mostly on other grounds, notably elevated digoxin levels in some of the corpses (evidence of poisoning?).
(28/45) “the hypothesis of digoxin poisoning was disproven [through new testing; similar to Susan Nelles case], the statistical data were biased and the analysis incorrect, and the conclusions drawn from it invalid.” • Case reopened June 2008. Not guilty verdict, April 2010. • Of course, she still might be guilty! (Mercy killings?) • But the statistical evidence wasn’t convincing.
de Berk Case: So What Happened?
• de Berk was convicted of multiple murders and attempted murders in March 2003, primarily on the basis of “1 in 342 million”. • The convictions were upheld on appeal, June 2004. • However, by the appeal date, enough doubts had been raised about the statistical calculations that the conviction was upheld mostly on other grounds, notably elevated digoxin levels in some of the corpses (evidence of poisoning?). • October 2007 Dutch “Posthumus II Commission” report:
(28/45) similar to Susan Nelles case], the statistical data were biased and the analysis incorrect, and the conclusions drawn from it invalid.” • Case reopened June 2008. Not guilty verdict, April 2010. • Of course, she still might be guilty! (Mercy killings?) • But the statistical evidence wasn’t convincing.
de Berk Case: So What Happened?
• de Berk was convicted of multiple murders and attempted murders in March 2003, primarily on the basis of “1 in 342 million”. • The convictions were upheld on appeal, June 2004. • However, by the appeal date, enough doubts had been raised about the statistical calculations that the conviction was upheld mostly on other grounds, notably elevated digoxin levels in some of the corpses (evidence of poisoning?). • October 2007 Dutch “Posthumus II Commission” report: “the hypothesis of digoxin poisoning was disproven [through new testing;
(28/45) the statistical data were biased and the analysis incorrect, and the conclusions drawn from it invalid.” • Case reopened June 2008. Not guilty verdict, April 2010. • Of course, she still might be guilty! (Mercy killings?) • But the statistical evidence wasn’t convincing.
de Berk Case: So What Happened?
• de Berk was convicted of multiple murders and attempted murders in March 2003, primarily on the basis of “1 in 342 million”. • The convictions were upheld on appeal, June 2004. • However, by the appeal date, enough doubts had been raised about the statistical calculations that the conviction was upheld mostly on other grounds, notably elevated digoxin levels in some of the corpses (evidence of poisoning?). • October 2007 Dutch “Posthumus II Commission” report: “the hypothesis of digoxin poisoning was disproven [through new testing; similar to Susan Nelles case],
(28/45) and the conclusions drawn from it invalid.” • Case reopened June 2008. Not guilty verdict, April 2010. • Of course, she still might be guilty! (Mercy killings?) • But the statistical evidence wasn’t convincing.
de Berk Case: So What Happened?
• de Berk was convicted of multiple murders and attempted murders in March 2003, primarily on the basis of “1 in 342 million”. • The convictions were upheld on appeal, June 2004. • However, by the appeal date, enough doubts had been raised about the statistical calculations that the conviction was upheld mostly on other grounds, notably elevated digoxin levels in some of the corpses (evidence of poisoning?). • October 2007 Dutch “Posthumus II Commission” report: “the hypothesis of digoxin poisoning was disproven [through new testing; similar to Susan Nelles case], the statistical data were biased and the analysis incorrect,
(28/45) • Case reopened June 2008. Not guilty verdict, April 2010. • Of course, she still might be guilty! (Mercy killings?) • But the statistical evidence wasn’t convincing.
de Berk Case: So What Happened?
• de Berk was convicted of multiple murders and attempted murders in March 2003, primarily on the basis of “1 in 342 million”. • The convictions were upheld on appeal, June 2004. • However, by the appeal date, enough doubts had been raised about the statistical calculations that the conviction was upheld mostly on other grounds, notably elevated digoxin levels in some of the corpses (evidence of poisoning?). • October 2007 Dutch “Posthumus II Commission” report: “the hypothesis of digoxin poisoning was disproven [through new testing; similar to Susan Nelles case], the statistical data were biased and the analysis incorrect, and the conclusions drawn from it invalid.”
(28/45) Not guilty verdict, April 2010. • Of course, she still might be guilty! (Mercy killings?) • But the statistical evidence wasn’t convincing.
de Berk Case: So What Happened?
• de Berk was convicted of multiple murders and attempted murders in March 2003, primarily on the basis of “1 in 342 million”. • The convictions were upheld on appeal, June 2004. • However, by the appeal date, enough doubts had been raised about the statistical calculations that the conviction was upheld mostly on other grounds, notably elevated digoxin levels in some of the corpses (evidence of poisoning?). • October 2007 Dutch “Posthumus II Commission” report: “the hypothesis of digoxin poisoning was disproven [through new testing; similar to Susan Nelles case], the statistical data were biased and the analysis incorrect, and the conclusions drawn from it invalid.” • Case reopened June 2008.
(28/45) • Of course, she still might be guilty! (Mercy killings?) • But the statistical evidence wasn’t convincing.
de Berk Case: So What Happened?
• de Berk was convicted of multiple murders and attempted murders in March 2003, primarily on the basis of “1 in 342 million”. • The convictions were upheld on appeal, June 2004. • However, by the appeal date, enough doubts had been raised about the statistical calculations that the conviction was upheld mostly on other grounds, notably elevated digoxin levels in some of the corpses (evidence of poisoning?). • October 2007 Dutch “Posthumus II Commission” report: “the hypothesis of digoxin poisoning was disproven [through new testing; similar to Susan Nelles case], the statistical data were biased and the analysis incorrect, and the conclusions drawn from it invalid.” • Case reopened June 2008. Not guilty verdict, April 2010.
(28/45) (Mercy killings?) • But the statistical evidence wasn’t convincing.
de Berk Case: So What Happened?
• de Berk was convicted of multiple murders and attempted murders in March 2003, primarily on the basis of “1 in 342 million”. • The convictions were upheld on appeal, June 2004. • However, by the appeal date, enough doubts had been raised about the statistical calculations that the conviction was upheld mostly on other grounds, notably elevated digoxin levels in some of the corpses (evidence of poisoning?). • October 2007 Dutch “Posthumus II Commission” report: “the hypothesis of digoxin poisoning was disproven [through new testing; similar to Susan Nelles case], the statistical data were biased and the analysis incorrect, and the conclusions drawn from it invalid.” • Case reopened June 2008. Not guilty verdict, April 2010. • Of course, she still might be guilty!
(28/45) • But the statistical evidence wasn’t convincing.
de Berk Case: So What Happened?
• de Berk was convicted of multiple murders and attempted murders in March 2003, primarily on the basis of “1 in 342 million”. • The convictions were upheld on appeal, June 2004. • However, by the appeal date, enough doubts had been raised about the statistical calculations that the conviction was upheld mostly on other grounds, notably elevated digoxin levels in some of the corpses (evidence of poisoning?). • October 2007 Dutch “Posthumus II Commission” report: “the hypothesis of digoxin poisoning was disproven [through new testing; similar to Susan Nelles case], the statistical data were biased and the analysis incorrect, and the conclusions drawn from it invalid.” • Case reopened June 2008. Not guilty verdict, April 2010. • Of course, she still might be guilty! (Mercy killings?)
(28/45) de Berk Case: So What Happened?
• de Berk was convicted of multiple murders and attempted murders in March 2003, primarily on the basis of “1 in 342 million”. • The convictions were upheld on appeal, June 2004. • However, by the appeal date, enough doubts had been raised about the statistical calculations that the conviction was upheld mostly on other grounds, notably elevated digoxin levels in some of the corpses (evidence of poisoning?). • October 2007 Dutch “Posthumus II Commission” report: “the hypothesis of digoxin poisoning was disproven [through new testing; similar to Susan Nelles case], the statistical data were biased and the analysis incorrect, and the conclusions drawn from it invalid.” • Case reopened June 2008. Not guilty verdict, April 2010. • Of course, she still might be guilty! (Mercy killings?) • But the statistical evidence wasn’t convincing. (28/45) Insider Lottery Wins
CBC Fifth Estate: 200 out of 5,713 major ($50,000+) Ontario lottery prizes from 1999–2006 were won by ticket sellers. Is that too many? Suspicious? (One case was already known . . . ) Using various different OLG figures, I computed that the expected number of major Ontario lottery wins that retail sellers should win was about 35, or 57, or . . . (Much less than 200!) Given this, the p-value (i.e., the probability that the sellers would win 200 or more major wins by pure luck alone) was between one chance in trillions of trillions, and one chance in ten billion. Extremely small! CONCLUSION: retail lottery sellers were definitely winning significantly more than could be explained by chance alone. So, there was indeed some lottery fraud! CBC broadcast scheduled for evening of Wed Oct 25 . . .
A Statistical Success:
(29/45) CBC Fifth Estate: 200 out of 5,713 major ($50,000+) Ontario lottery prizes from 1999–2006 were won by ticket sellers. Is that too many? Suspicious? (One case was already known . . . ) Using various different OLG figures, I computed that the expected number of major Ontario lottery wins that retail sellers should win was about 35, or 57, or . . . (Much less than 200!) Given this, the p-value (i.e., the probability that the sellers would win 200 or more major wins by pure luck alone) was between one chance in trillions of trillions, and one chance in ten billion. Extremely small! CONCLUSION: retail lottery sellers were definitely winning significantly more than could be explained by chance alone. So, there was indeed some lottery fraud! CBC broadcast scheduled for evening of Wed Oct 25 . . .
A Statistical Success: Insider Lottery Wins
(29/45) Is that too many? Suspicious? (One case was already known . . . ) Using various different OLG figures, I computed that the expected number of major Ontario lottery wins that retail sellers should win was about 35, or 57, or . . . (Much less than 200!) Given this, the p-value (i.e., the probability that the sellers would win 200 or more major wins by pure luck alone) was between one chance in trillions of trillions, and one chance in ten billion. Extremely small! CONCLUSION: retail lottery sellers were definitely winning significantly more than could be explained by chance alone. So, there was indeed some lottery fraud! CBC broadcast scheduled for evening of Wed Oct 25 . . .
A Statistical Success: Insider Lottery Wins
CBC Fifth Estate: 200 out of 5,713 major ($50,000+) Ontario lottery prizes from 1999–2006 were won by ticket sellers.
(29/45) Suspicious? (One case was already known . . . ) Using various different OLG figures, I computed that the expected number of major Ontario lottery wins that retail sellers should win was about 35, or 57, or . . . (Much less than 200!) Given this, the p-value (i.e., the probability that the sellers would win 200 or more major wins by pure luck alone) was between one chance in trillions of trillions, and one chance in ten billion. Extremely small! CONCLUSION: retail lottery sellers were definitely winning significantly more than could be explained by chance alone. So, there was indeed some lottery fraud! CBC broadcast scheduled for evening of Wed Oct 25 . . .
A Statistical Success: Insider Lottery Wins
CBC Fifth Estate: 200 out of 5,713 major ($50,000+) Ontario lottery prizes from 1999–2006 were won by ticket sellers. Is that too many?
(29/45) (One case was already known . . . ) Using various different OLG figures, I computed that the expected number of major Ontario lottery wins that retail sellers should win was about 35, or 57, or . . . (Much less than 200!) Given this, the p-value (i.e., the probability that the sellers would win 200 or more major wins by pure luck alone) was between one chance in trillions of trillions, and one chance in ten billion. Extremely small! CONCLUSION: retail lottery sellers were definitely winning significantly more than could be explained by chance alone. So, there was indeed some lottery fraud! CBC broadcast scheduled for evening of Wed Oct 25 . . .
A Statistical Success: Insider Lottery Wins
CBC Fifth Estate: 200 out of 5,713 major ($50,000+) Ontario lottery prizes from 1999–2006 were won by ticket sellers. Is that too many? Suspicious?
(29/45) Using various different OLG figures, I computed that the expected number of major Ontario lottery wins that retail sellers should win was about 35, or 57, or . . . (Much less than 200!) Given this, the p-value (i.e., the probability that the sellers would win 200 or more major wins by pure luck alone) was between one chance in trillions of trillions, and one chance in ten billion. Extremely small! CONCLUSION: retail lottery sellers were definitely winning significantly more than could be explained by chance alone. So, there was indeed some lottery fraud! CBC broadcast scheduled for evening of Wed Oct 25 . . .
A Statistical Success: Insider Lottery Wins
CBC Fifth Estate: 200 out of 5,713 major ($50,000+) Ontario lottery prizes from 1999–2006 were won by ticket sellers. Is that too many? Suspicious? (One case was already known . . . )
(29/45) that retail sellers should win was about 35, or 57, or . . . (Much less than 200!) Given this, the p-value (i.e., the probability that the sellers would win 200 or more major wins by pure luck alone) was between one chance in trillions of trillions, and one chance in ten billion. Extremely small! CONCLUSION: retail lottery sellers were definitely winning significantly more than could be explained by chance alone. So, there was indeed some lottery fraud! CBC broadcast scheduled for evening of Wed Oct 25 . . .
A Statistical Success: Insider Lottery Wins
CBC Fifth Estate: 200 out of 5,713 major ($50,000+) Ontario lottery prizes from 1999–2006 were won by ticket sellers. Is that too many? Suspicious? (One case was already known . . . ) Using various different OLG figures, I computed that the expected number of major Ontario lottery wins
(29/45) was about 35, or 57, or . . . (Much less than 200!) Given this, the p-value (i.e., the probability that the sellers would win 200 or more major wins by pure luck alone) was between one chance in trillions of trillions, and one chance in ten billion. Extremely small! CONCLUSION: retail lottery sellers were definitely winning significantly more than could be explained by chance alone. So, there was indeed some lottery fraud! CBC broadcast scheduled for evening of Wed Oct 25 . . .
A Statistical Success: Insider Lottery Wins
CBC Fifth Estate: 200 out of 5,713 major ($50,000+) Ontario lottery prizes from 1999–2006 were won by ticket sellers. Is that too many? Suspicious? (One case was already known . . . ) Using various different OLG figures, I computed that the expected number of major Ontario lottery wins that retail sellers should win
(29/45) (Much less than 200!) Given this, the p-value (i.e., the probability that the sellers would win 200 or more major wins by pure luck alone) was between one chance in trillions of trillions, and one chance in ten billion. Extremely small! CONCLUSION: retail lottery sellers were definitely winning significantly more than could be explained by chance alone. So, there was indeed some lottery fraud! CBC broadcast scheduled for evening of Wed Oct 25 . . .
A Statistical Success: Insider Lottery Wins
CBC Fifth Estate: 200 out of 5,713 major ($50,000+) Ontario lottery prizes from 1999–2006 were won by ticket sellers. Is that too many? Suspicious? (One case was already known . . . ) Using various different OLG figures, I computed that the expected number of major Ontario lottery wins that retail sellers should win was about 35, or 57, or . . .
(29/45) Given this, the p-value (i.e., the probability that the sellers would win 200 or more major wins by pure luck alone) was between one chance in trillions of trillions, and one chance in ten billion. Extremely small! CONCLUSION: retail lottery sellers were definitely winning significantly more than could be explained by chance alone. So, there was indeed some lottery fraud! CBC broadcast scheduled for evening of Wed Oct 25 . . .
A Statistical Success: Insider Lottery Wins
CBC Fifth Estate: 200 out of 5,713 major ($50,000+) Ontario lottery prizes from 1999–2006 were won by ticket sellers. Is that too many? Suspicious? (One case was already known . . . ) Using various different OLG figures, I computed that the expected number of major Ontario lottery wins that retail sellers should win was about 35, or 57, or . . . (Much less than 200!)
(29/45) was between one chance in trillions of trillions, and one chance in ten billion. Extremely small! CONCLUSION: retail lottery sellers were definitely winning significantly more than could be explained by chance alone. So, there was indeed some lottery fraud! CBC broadcast scheduled for evening of Wed Oct 25 . . .
A Statistical Success: Insider Lottery Wins
CBC Fifth Estate: 200 out of 5,713 major ($50,000+) Ontario lottery prizes from 1999–2006 were won by ticket sellers. Is that too many? Suspicious? (One case was already known . . . ) Using various different OLG figures, I computed that the expected number of major Ontario lottery wins that retail sellers should win was about 35, or 57, or . . . (Much less than 200!) Given this, the p-value (i.e., the probability that the sellers would win 200 or more major wins by pure luck alone)
(29/45) Extremely small! CONCLUSION: retail lottery sellers were definitely winning significantly more than could be explained by chance alone. So, there was indeed some lottery fraud! CBC broadcast scheduled for evening of Wed Oct 25 . . .
A Statistical Success: Insider Lottery Wins
CBC Fifth Estate: 200 out of 5,713 major ($50,000+) Ontario lottery prizes from 1999–2006 were won by ticket sellers. Is that too many? Suspicious? (One case was already known . . . ) Using various different OLG figures, I computed that the expected number of major Ontario lottery wins that retail sellers should win was about 35, or 57, or . . . (Much less than 200!) Given this, the p-value (i.e., the probability that the sellers would win 200 or more major wins by pure luck alone) was between one chance in trillions of trillions, and one chance in ten billion.
(29/45) CONCLUSION: retail lottery sellers were definitely winning significantly more than could be explained by chance alone. So, there was indeed some lottery fraud! CBC broadcast scheduled for evening of Wed Oct 25 . . .
A Statistical Success: Insider Lottery Wins
CBC Fifth Estate: 200 out of 5,713 major ($50,000+) Ontario lottery prizes from 1999–2006 were won by ticket sellers. Is that too many? Suspicious? (One case was already known . . . ) Using various different OLG figures, I computed that the expected number of major Ontario lottery wins that retail sellers should win was about 35, or 57, or . . . (Much less than 200!) Given this, the p-value (i.e., the probability that the sellers would win 200 or more major wins by pure luck alone) was between one chance in trillions of trillions, and one chance in ten billion. Extremely small!
(29/45) So, there was indeed some lottery fraud! CBC broadcast scheduled for evening of Wed Oct 25 . . .
A Statistical Success: Insider Lottery Wins
CBC Fifth Estate: 200 out of 5,713 major ($50,000+) Ontario lottery prizes from 1999–2006 were won by ticket sellers. Is that too many? Suspicious? (One case was already known . . . ) Using various different OLG figures, I computed that the expected number of major Ontario lottery wins that retail sellers should win was about 35, or 57, or . . . (Much less than 200!) Given this, the p-value (i.e., the probability that the sellers would win 200 or more major wins by pure luck alone) was between one chance in trillions of trillions, and one chance in ten billion. Extremely small! CONCLUSION: retail lottery sellers were definitely winning significantly more than could be explained by chance alone.
(29/45) CBC broadcast scheduled for evening of Wed Oct 25 . . .
A Statistical Success: Insider Lottery Wins
CBC Fifth Estate: 200 out of 5,713 major ($50,000+) Ontario lottery prizes from 1999–2006 were won by ticket sellers. Is that too many? Suspicious? (One case was already known . . . ) Using various different OLG figures, I computed that the expected number of major Ontario lottery wins that retail sellers should win was about 35, or 57, or . . . (Much less than 200!) Given this, the p-value (i.e., the probability that the sellers would win 200 or more major wins by pure luck alone) was between one chance in trillions of trillions, and one chance in ten billion. Extremely small! CONCLUSION: retail lottery sellers were definitely winning significantly more than could be explained by chance alone. So, there was indeed some lottery fraud!
(29/45) A Statistical Success: Insider Lottery Wins
CBC Fifth Estate: 200 out of 5,713 major ($50,000+) Ontario lottery prizes from 1999–2006 were won by ticket sellers. Is that too many? Suspicious? (One case was already known . . . ) Using various different OLG figures, I computed that the expected number of major Ontario lottery wins that retail sellers should win was about 35, or 57, or . . . (Much less than 200!) Given this, the p-value (i.e., the probability that the sellers would win 200 or more major wins by pure luck alone) was between one chance in trillions of trillions, and one chance in ten billion. Extremely small! CONCLUSION: retail lottery sellers were definitely winning significantly more than could be explained by chance alone. So, there was indeed some lottery fraud! CBC broadcast scheduled for evening of Wed Oct 25 . . . (29/45) Globe & Mail Front Page, Oct. 25, 2006
(30/45) Toronto Sun
(31/45) Toronto Star
(32/45) Globe & Mail Editorial
(33/45) Toronto Sun (p. 4)
(34/45) “$100 million to lottery insiders”
Ombudsman:
(35/45) Ombudsman: “$100 million to lottery insiders”
(35/45) Heads Roll!
(36/45) New Rules For Signing and Checking Tickets
(37/45) The Police Investigate
(38/45) And Make Arrests!
(39/45) $5.7 Million Repaid to Rightful Winner!
(40/45) Another $80,000 Repaid!
(41/45) Later, Three More Retailers Charged . . .
(42/45) Could the True Winners be Found?
(43/45) Found them! (January 2011)
(44/45) And It All Followed From Statistics!
(45/45) And It All Followed From Statistics!
(45/45)