A psychologist has tested 25 independent hypotheses. The 25 unadjusted p-values

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?

Explanation / Answer

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

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.

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

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