Power Analyses for Minimum-Effect Tests
The traditional null hypothesis is that treatments or interventions have no effect; in Chapters 1 and 2, we use the term “nil hypothesis” to describe this particular version of H0. However, null hypotheses are not limited to the hypothesis that treatments or interventions have no effect. The null hypothesis is simply the specific hypothesis that is being tested (and that might be nullified by the data), and there are an infinite number of null hypotheses researchers might test. One researcher comparing two treatments might test the hypothesis that there is no difference between the mean scores of people who receive different treatments. A different researcher might test the hypothesis that one treatment yields scores that are, on average, five points higher than those obtained using another treatment. Yet another researcher might test the hypothesis that treatments have a very large effect, accounting for at least 25% of the variance in outcomes. These are all null hypotheses. Knowing that there are so many null hypotheses that might be tested, it is useful to understand why one special form-i.e., the nil hypothesis-is the one that actually is tested in most statistical analyses.