Page "Statistical power" Paragraph 15

Any statistical analysis involving multiple hypotheses is subject to inflation of the type I error rate if appropriate measures are not taken.

Such measures typically involve applying a higher threshold of stringency to reject a hypothesis in order to compensate for the multiple comparisons being made ( e. g. as in the Bonferroni method ).

In this situation, the power analysis should reflect the multiple testing approach to be used.

Thus, for example, a given study may be well powered to detect a certain effect size when only one test is to be made, but the same effect size may have much lower power if several tests are to be performed.