Psychologists once measured 77 variables on a sample of schizophrenic people and

Question

Psychologists once measured 77 variables on a sample of schizophrenic people and a sample of people who were not schizophrenic. They compared the two samples using 77 separate significance tests. Two of these tests were significant at the 5% level. Suppose that there is in fact no difference in any of the 77 variables between people who are and people who are not schizophrenic in the adult population. That is, all 77 null hypotheses are true. (a) What is the probability that one specific test shows a difference that is significant at the 5% level? (b) Why is it not surprising that 2 of the 77 tests were significant at the 5% level? Think of a Binomial random variable.

Explanation / Answer

A) What is the probability that one specific test shows a difference that is significant at the 5% level?

The probability is 5%

B) Why is it not surprising that 2 of the 77 tests were significant at the 5% level?

It's not surprising because 5% of 77 is 3.85, So we expect almost 4 observations to be significantat the 5% level. These two observations could be two of these four.

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