A statistical methodology for conducting multiple comparisons

The important point to note here is that the a = 0.05 level is deemed appropriate when a single test is being conducted. Multiple comparisons, by definition, mean that more that one test is being conducted. When testing a number of pairwise comparisons - for example, after an ANOVA where the null hyqiothesis has been rejected - it is not acceptable to test each pairwise comparison at the a = 0.05 level because of the potential inflation of the overall type I error rate. 

That is, instead of a type I error rate of a = 0.05, this analysis has resulted in a higher probability of committing a type I error, just by chance alone. 

In fact, the comparisons made here cannot be thought of as independent because each group is compared with two others in this case. It is more correct to use an inequality sign to say that the probability is no more than 0.14, that is, 0.14. However, this technicality is of little comfort because, to make sound decisions, we would really like to limit that probability to a reasonable level. In general, if C comparisons are each made at the a level, the probability of rejecting at least one by chance alone is  

of hypotheses tested at a = 0.05 Maximum probability of type 1 error 

Chapter 1 1 Confirmatory clinical trials Analysis of continuous efficacy data 

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