Shuffle to test a difference

Use random assignments to understand how surprising a difference is.

Hold the scores fixed

Four participants score 1, 2, 3 and 4. Conditions A and B were assigned at random, two people per condition. A has 3 and 4, so the mean difference A − B is 3.5 − 1.5 = 2.

Assume neither condition changes anyone’s score. Under this assumption, the same scores could have received different labels. Choose any two of the four participants for A: there are C(4, 2) = 6 equally likely assignments.

AB3412A − B = 2
Same scores, different labels.

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First lesson in this subject: Read data before calculating

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