AIM: We Will Not Fear Statistics!

BHS Name______AP PSYCH

AIM: We will not fear statistics!

There are different ways that psychologists can show data and describe it for the specific group studied. This is known as descriptive statistics.

A. One way to describe data is to show someone as being in a certain percentile. If a person is in the 74th percentile, this means 74% of students performed lower. Describe the percentiles of the following students. a. Mary i. 20th percentile Math______

ii. 58th percentile English______

iii. Which subject can we infer that Mary is better in?______Why?

b. Joe i. 85th percentile Math______

ii. 45th percentile English______

iii. Which subject can we infer that Joe is better in? ______Why?

B. MEASURES OF CENTRAL TENDANCY (a single number that represents a whole set of scores) a. 3 Ms i. MEAN

ii. MEDIAN

iii. MODE

C. Skewed distributions a. The MEAN is the ______; however, it is the MOST ______to outliers or extreme scores.

In a normal distribution, the measures of central tendency tend to fall in the middle

b. In a POSITIVE or RIGHT SKEW… the MEAN is pulled ______because the outliers or extreme scores are on the upper data points of x- axis. Yet, the bulk of the scores are on the lower data points of x-axis. If this were test data, we could conclude that, the majority did ______, and a few outliers ______

c. In a NEGATIVE or LEFT SKEW… the MEAN is pulled

______because the outliers or extreme scores are on the lower data points of x-axis. Yet, the bulk of the scores are on the upper data points of x-axis. If this were test data, we could conclude that, the majority did ______and a few outliers ______

**MEMORY TIP! The “tail” of the skewed distribution graph points to the type of skew (tail pointing the left=negative skew; tail pointing to the right=positive skew). This will help you remember what happens to the mean in skewed distributions… Typically, in these cases, the MEDIAN is more accurate reflection of group than the mean.

D. Dispersion or spread of scores (define) a. Range

b. Variance

c. Standard Deviation

1. Two classes took the same psychology test. The scores for the first period class were: 81, 85, 94, 88, 80, 77, and 90. The scores for the second period class were: 55, 105, 92, 73, 95, 95, and 80. Which group has the greater standard deviation? (I do not expect you to do any calculations)

2. IQ (intelligence quotient) scores are normally distributed with a mean of 100 and a standard deviation of 16. What percentage of people have scores above 116?

3. What statistical technique would be appropriate for a researchers to use in trying to determine how consistent intelligent scores are over time? a. coefficient; b. mean; c. median; d. range; e. standard deviation

4. When a distribution of scores is skewed, the best representation of the central tendency is the: a. Standard deviation; b. mean; c. median; d. coefficient Using the bell curve provided... 1. Examine the Weschler Adult Intelligence (top) scale scores. What is the standard deviation?______points 2. Examine the SAT Math scale scores (below). What is the standard deviation?______points 3. Which has a higher standard deviation: SAT or IQ test? What does this mean?

4. If your SCORE is 800 on the SAT Math Scale, how many standard deviations (z-scores) are you from the mean?______5. What is the SCORE one standard deviation above the mean on the Wechsler Adult Intelligence Scale?______the Z score is:______6. What is the SCORE one standard deviation below the mean on the SAT Math Scale? _____ The Z score is:___ E. The Empirical Rule or “68-95-99 Rule”

Pretend the mean is a 75% on an AP test. The standard deviation is 5. Draw what the curve might look like. Draw at least two standard deviations away from the mean.

What does a Z score of +1 equal?______What about -2______? (tells us how far away score is from the mean) What does that say about the scores of 68% of the class? They scored between _____ and ______. What about 95% of class? They scored between ______and ______What % of class scores were above 85%?______II. Inferential statistics : The researcher can INFER about the POPULATION based on what is known about the sample.

Statistics is a measure for a sample (n).

Parameter is a measure for the population (N).

Is the data for sample (n) descriptive of the population (N)? We will never know, but we make an inference. The larger the sample, the more representative, the more reliable.

F. Statistical significance  The results were not due to CHANCE  If p is LOW, .05 or .04 or .03 or .02 or .01  WE CAN REJECT NULL! The null hypothesis is what the researcher tries to disprove, reject, or nullify. **You can never 100% fully prove anything in science; you can only reject the null hypothesis, which is the opposite of the hypothesis (you can only disprove, not prove). You can’t prove anything is 100% true because you can never know if it was 100% not due to chance (never a 0% p-value) BUT if the p-value is less that .05%, you can be confident enough (statistically significant)

NULL: (H0) A new vaccine does not change the proportion of people with a fever ALTERNATIVE: (H1) A new vaccine has a LOWER proportion of people with a fever p value = .0139 -What can we conclude?

H0: The new treatment does not improve mental health H1: The new treatment does improve mental health p value = .06 What can we conclude?

5. Basketball team data is as follows – calculate the measures of central tendency and draw a frequency histogram. Does it have a positive or negative SKEW?

Jake 14 points Scott 4 points Josh 22 points Bobby 6 points Christian 19 points Grant 8 points Billy 3 points Thomas 6 points