STUDIES IN RESEARCH METHODOLOGY:V IRRELEVANCE IN THE + TEST’S REJECTION REGION

摘要

The most desirable "rejection region" (unobtainable in practice) would consist of those t's having the most extreme sample means in their numerators, since the sample mean is the best and most direct indicator of the value of the population mean, which is the hypothesis under test. Instead, the rejection region consists of the most extreme t ratios, some of which are extreme, not because of an extreme Y in their numerators, but rather due to the effect of a very small s in their denominators. Such t's are "irrelevant" in the sense that rejection is due to the chance value of a variable which has no useful relationship with the hypothesis under test, i.e. no predictive relationship with the population mean. The presence of irrelevant t's in the rejection region can only be detrimental to the power of the test. This report shows that the proportion of irrelevant t's in the t test's rejection region diminishes with increasing sample size and is inversely related to the size, a , of the significance level used. Irrelevance virtually disappears at very large sample sizes;however, it is quite appreciable at the sample sizes commonly used in psychological experiments.