On more powerful tests of judge agreement with a known standard

To establish the existence of his abilities, a judge is given the task of classifying each ofN=rs subjects into one ofr known categories, each containings of the subjects. An incomplete design is proposed whereby the judge is presented withb groups, each one containingn=rs/b<r subjects. Then different categories corresponding to members of the group are known. Using the total number of correct classifications, this method of grouping is compared to that in which the group size is equal to the number of categories. The incomplete grouping is shown to yield a more powerful test for discriminating between the null hypothesis that the judge is guessing the classifications and the alternative hypothesis that he has some definite abilities. The incomplete design is found to be most effective (powerful) when the number of subjects in a group is limited to two or three.The author is grateful for the suggestions of the referees and the editor, which greatly improved the paper.