An Analysis of Variance of Multiple Measurements on Subjects Classified in Unequal Groups of One Dimension

IN EXPERIMENTS where more than one measurement is taken on a subject, special an alysis is required because of the lack of statis tical independence among the measurements . Typical of such experiments are those in which subjects are first categorized into one of sever al different groups. Thereafter, multiple meas urements are made on each subject under condi tions corresponding to all combinations of o n e or more ways of classification. Various writers have viewed aspects of the multiple measurements problem. The founda tions were laid by Yates (8, 9,10) in his early papers on the split-plot design which has been used extensively in agricultural experimentation. Among the more recent work on this general problem has been that by Moonan (5, 6), Hoy t, Stunkard, etal.,(3), Kogan (4), Halperin (2), and Collier (?J1 This paper considers the model and analysis of a design in which subjects are classified into several groups with possibly un equal frequencies along one classification dimen sion. Then, each subject is measured under all combinations of a further two-way classification system.