Bonferroni The problem of multiple tests of significance. In many kinds of research, particularly surveys and studies using batteries of tests, and with certain statistical methods (such as multiple regression and analysis of variance), there are frequently many (more than, say, 10) statistical hypotheses being tested (perhaps on different dependent and independent variable combinations). In such studies, we find that setting = 0.05 does not provide sufficient protection against the Type I error. What happens is that as the number of separate hypothesis tests increase within a single study, the true -level for the entire study (regardless of where you think you have set it) will be inflated . An approximate formula for how much increases as a function of the number of hypotheses you test is actual -level = 1 - (1- you think you are setting) j where j is the number of significance tests being done or contemplated. Thus, if we think we are setting at 0.05 in our study, but we are contemplating testing 20 statistical hypotheses (say 20 t-tests), our actual chance of claiming a significant result when there should not be one is 1 - (1 - 0.05)20 = 0.64. That is, we really have a 64% chance of making a Type I error. This is quite a substantial chance!! Moreover, you do not know which ones are errors and which ones arenOt. There are a couple of ways of coping with this problem in multivariate studies. The best way is to use special