Discriminant Analysis: A Comment.
The frequent incorrect application or interpretation of statistical methods in publications that use statistics has been noted by a number of authors (e.g., Altman, 1982; Bartko, 1986; Fletcher, Rice, & Ray, 1978; Oakes, 1986; Strube & Hartmann, 1982; Wade & Hartmann, 1978; White, 1979). Bartko indicated, for example, that about half of publications of this type examined in several recent reviews had statistical errors ranging from minor to major, "including false conclusions" (p. 1199). More recently, the frequent occurrence of statistical errors in substantive articles refereed by Long led him to devote an entire book to this subject (Long, 1988). Perhaps as a consequence of the growing awareness of the problem, articles that attempt to inform researchers about statistical methods and promote their correct use have been appearing with increasing frequency in most of the empirical journals of the American Psychological Association. Betz's (1987) recent article on the use of discriminant function analysis in counseling psychology research is of this type. Betz noted that "it is hoped that [the article] will increase readers' interest in and ability to appropriately use discriminant analysis [DA]" (p. 402). The article, in fact, correctly and accurately describes many features of DA that are of use to researchers in counseling psychology. However, there are also some sections of Betz's article that may result in misinterpretation or misapplication of DA. These sections are concerned with (a) methods of testing the significance of discriminant function weights, (b) goals of classification rules, and (c) methods of testing the significance of differences between observed and chance total hit rates. In this article I present information related to these topics and hope to increase the likelihood of the correct application and interpretation of DA. The first topic is considered more important, and is consequently discussed in more detail, than either the second or third topics.