Simultaneous Statistical Tests on Categorical Data

Abstract

THE QUESTION Data collected for. purposes of education re search frequently are of the categorical type to which may be applied the classical tests for in dependence in contingency tables or tests for good ness-of-fit of empirical to hypothetical frequency distributions. It is not uncommon, for example, that a number of respondents answer avariety of questions on a given questionnaire which then is sum marized by way of a number of two-way contingency tables of interest to the investigation. The problem which arises in this context is the following. Gen erally the several resulting test statistics will be correlated because the same respondents are in volved. As a consequence, the conclusions reached upon performing one statistical test may depend on those obtained through another test. Thus it is mis leading to compare each test statistic separately in the usual manner with a critical point from the Chi square (x2) distribution which would be appropriate if the hypotheses could be tested independently. Re fer to Miller [ 3] for a general discussion.