Question

A psychologist has tested 25 independent hypotheses. The 25 unadjusted p-values she obtained are as follows: 0.0042, 0.3303, 0.0025, 0.0018, 0.00001, 0.8329, 0.0002, 0.1364, 0.0006, 0.0407, 0.1523, 0.0022, 0.2276, 0.0014, 0.0036, 0.0123, 0.3103, 0.0067, 0.8628, 0.6282, 0.0053, 0.00003, 0.0173, 0.4636, and 0.0082. Which, if any, hypotheses can she reject controlling the false discovery rate at 0.05? Which, if any, hypotheses can she reject controlling the experimentwise error rate at no more than 0.05?

Answer 1

If we arrange the given p-values in ascending order, we have below data

Sr. No.	p-values
1	0.00001
2	0.00003
3	0.0002
4	0.0006
5	0.0014
6	0.0018
7	0.0022
8	0.0025
9	0.0036
10	0.0042
11	0.0053
12	0.0067
13	0.0082
14	0.0123
15	0.0173
16	0.0407
17	0.1364
18	0.1523
19	0.2276
20	0.3103
21	0.3303
22	0.4636
23	0.6282
24	0.8329
25	0.8628

In the above data, first 16 values are less than 0.05, hence we reject the null hypothesis in all those 16 cases.

experiment error wise rate is alpha, which is 0.05. Again same 16 hypothesis were rejected.