ADDENDUM TO BUCKALEW'S "NONPARAMETRICS AND PSYCHOLOGY: A REVITALIZED ALLIANCE"'

This note is wrirten in the same spirit as Buckalew's (1983) recent paper, extending his arguments to modern developments in analysis of multidimensional contingency tables and in nonparametric rank analysis of variance. Widespread awareness of the existence of these methodological advances would help diminish the concerns psychologists may have about purported limitations of nonparametric statistics to which he alluded. When post hoc multiple comparisons associated with classical analysis of variance are applied to quantitative research data, an omnibus F test is sometimes computed first, followed by specific tests of contrasts. If ScheffC's method is used, a statistically significant omnibus F value implies that at least one of the contrasts will also be significant. Over the last two decades, Goodman (1978) and his coworkers have developed "ScheffClike" procedures for application to multidimensional contingency tables. The Goodman statistic is based on a log-linear model analogous to the fixed-effects model of ordinary analysis of variance. This means that for contingency tables containing r rows, c columns, e experimental groups, and so on, Goodman's technique can be used to perform tests of main effects and interactions. Since the computations required with the log-linear model are tedious, chis procedure cannot be subsumed under the "quick and dirty" designation often mentioned in connection with nonparametric techniques such as the sign test and the median test. Fortunately, Goodman and his colleagues at the University of Chicago have written a computer program entitled Everyman's Contingency Table Analysis (ECTA) which has been widely distributed. A brief introduction to the log-linear model, including a worked example for a three-dimensional table, has been given by Hays (1981, pp. 561-566). One shortcoming of the Goodman test, which it shares with ScheffC's test, is that it is relatively insensitive, since it controls the experimentwise error rate so that the investigator can test all contrasts which are of interest, even ones which are suggested by inspection of the data. If a psychologist's research is based on strong theoretical underpinnings, so that a small, carefully selected set of questions or hypotheses can be formulated, it is advantageous instead to employ the Dunn-Bonferroni test, since it is more powerful (Marascuilo & McSweeney, 1977). For two-dimensional contingency tables a "coefficient of determination" for qualitative data is now available (Light, 1973). It is essentially a ratio of between sum of squares to total sum of squares and hence can be interprered as a proportion of explained variance in a way analogous to the correlation ratio of analysis of variance. This statistic is easy to compute and interpret and is more powerful than the traditional chi-squared test of homogeneity. Light's (1973) chapter contains a series of 14 illustrative numerical examples, one of which is an extension of the above-mentioned measure of association to a three-dimensional contingency table. These qualitative statistical models should be of particular interest to social scientists conducting observational studies, since data from such studies are often frequencies or proportions.