ABSTRACT
Descriptive measures in global CFA have not been discussed until very recently, when von Eye and Gutiérrez-Peña (in preparation) proposed using two measures descriptively that have also been used in efforts of Bayesian data mining (DuMouchel, 1999). The consideration of descriptive measures can be useful for four reasons. First, the measures discussed here are most intuitive and can easily be interpreted. Second, these measures are sensitive to different data characteristics than the residual-based statistics discussed in Chapter 2 of this volume. The differences between measures are discussed below. Third, the measures do not require assumptions concerning sampling schemes or approximations of sampling distributions. Thus, they are useful under almost any condition. Fourth, because these measures are used descriptively and in an exploratory context, they are particularly useful when tables are sparse and the significance tests cannot be trusted any more, or when tables are so large that the adjusted significance levels are prohibitively small. DuMouchel (1999) illustrated the use of these measures in tables with over 1.4 million cells. The Bonferroni-adjusted α for a table of this size is α* = 3.57E−8, a value that can be exceeded only with very large samples (or extremely small expected cell frequencies).
