When more than one hypothesis test is performed to make a binary decision, the chance of a false positive is usually greater than the size of any of the tests used for that decision. For example, suppose groups of "control" and "treatment" subjects are randomly selected from the same population and each subject is given a questionnaire comprising 20 yes-no questions. Let the groups be compared separately for each question using a test of size .05. If the comparisons are independent, then the chance of at least one of them rejecting the null equals $1 - (1 - 0.05)^{20}$ = 0.64. Thus a nominal false positive rate of 0.05 in each test is inflated to a decision false positive rate of 0.64.