stylistic:style_transfer, information:filtering, information:highlighting, linguistic:paraphrasing
Discussion

Additional complications arise when we consider these multiple hypotheses together. For example, if we consider a false positive to be making an erroneous null rejection on any one of these hypotheses, our likelihood of this "family-wise error" will be inflated if appropriate measures are not taken. Such measures typically involve applying a higher threshold of stringency to reject a hypothesis (such as with the Bonferroni method), and so would reduce power. Alternatively, there may be different notions of power connected with how the different hypotheses are considered. "Complete power" demands that all true effects are detected across all of the hypotheses, which is a much stronger requirement than the "minimal power" of being able to find at least one true effect, a type of power that might increase with an increasing number of hypotheses.