Key Concepts on Hypothesis Testing (A Decision Making Procedure)

Similarity to the justice system:

Hypothesis Testing Justice Procedures Purpose To prove the alternative hypothesis To prove a suspect guilty Step 1 Null vs Alternative hypothesis Innocence vs. Guilty Step 2 Evaluate the evidence from data Evaluate the evidence Step 3 Make a decision Jury hand out the decision

Note: 1. The procedure is provoked only when you believe the alternative is true (prosecutors do not select random persons for trials) and would like to get some evidence to support it. 2. The step 2 is objective (evidence is evidence) but the step 3 (handing out the decision) is subjective. 3. Mathematical evaluation of the evidence follows the same common sense logic as in the Ping Pong ball example.

Ping Pong Ball Example:

The original claim: 4 white balls and 1 yellow ball in the bag Observed: Three random draws (with replacement) gave three yellow balls

Conclusion (with your common sense): There should be more than one yellow balls in the bag, e.g. the original claim is wrong.

Your common sense logic being formalized: Given that the original claim is true, although it is possible to observe three yellow balls in three random draws, the chance of seeing it happening is too small (in fact, the chance is 1/125), therefore, the original claim should be wrong.

Lesson learned: In hypothese procedure, we evaluate the evidence by calculating how likely to seeing the evidence (3 yellow balls in three random draws) under the null hypothesis (4 white and 1 yellow balls in the bag).