Tests for factor differences when the numbers of items in the sub-classes are unequal
The analysis of variance, when used as a technique for testing hypotheses, constitutes an effective method for testing the homogeneity of a set of means of groups to which various experimental treatments have been administered. However, when the homogeneity hypothesis is rejected, the analysis of variance proves inadequate in that it does not designate where the differences between means exist. An indication of such differences is often required in order to evaluate the effects of the individual treatments. The problem of breaking up the treatment means into distinguishable groups, so as to indicate where the contrasts exist, has been investigated, to some extent, in the case of means based on treatment groups of equal numbers of items. The several approaches, and their corresponding statistical tests, will be reviewed. This will serve to introduce the general problem, and will provide a background for the case of means based upon groups of unequal numbers of items. Tests for this latter case will be proposed and presented with the tables necessary for the calculations entailed. Examples will be included.
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