ABSTRACT
This chapter introduces readers to the statistical tests that can be used to come to a decision as to whether a configuration constitutes a type, an antitype, or remains inconspicuous. Interestingly, the selection of tests in CFA has more facets than usually involved in the selection of statistical tests. One facet is, as one might expect, the statistical power of the available tests. A second facet concerns the conditions (sampling scheme) under which tests can be employed. A third facet, most important in the context of CFA and only rarely discussed thus far, is the kind of type and antitype researchers are interested in. We present tests that cover a number of the ways to deviate from independence or, in general, a CFA base model. The present chapter covers tests for global base models that can also be used in most regional base models. We begin with the binomial test and its approximations. This is followed by the χ2 and its approximations, and a section on tests that can be used when the margins are fixed as is the case in product-multinomial sampling. These tests will then be compared using results from simulation studies and an empirical data example. The presentation of significance tests is completed with a discussion of statistical power. There are additional tests that can be used only in two-sample CFA. These tests will be introduced in Section 7.2.
