Planned and Post Hoc Comparisons in Tests of Concordance and Discordance forG Groups of Judges

Statistical procedures for making comparisons on the ranking of a set ofK elements, wines, people, and so forth, have been worked out for the case in which the ranking is done by a single group ofn people. In this special situation, Friedman’s test can be called upon to assess the significance of differences in mean ranking, and Kendall’s coefficient of concordance can be used to measure the level of agreement among the individuals doing the ranking. Unfortunately, the problem of comparingG groups of subjects to determine whether or not they produce the same mean ranking has, until recently, remained unanswered. A procedure was developed for testing two-group concordance by Schucany and Frawley. Hollander and Sethuraman have questioned this procedure and have provided an alternative model for investigating the same problem. It is easy to show that the Schucany and Frawley model tests for positive rank correlation in the mean ranks as an alternative, whereas the Hollander and Sethuraman model tests identity of mean ranks across theK compared elements as the null. In this article, these two models are examined, the criticism is evaluated, and both models are extended to theG group situation. The extension to planned and post hoc comparisons is illustrated using data based on a study described by Marascuilo and Dagenais.