Multiple Classification Analysis for Arbitrary Experimental Arrangements

Usually an experiment is designed so as to be as balanced as possible which, among other things, simplifies the analysis of the results. However, if an appreciable number of planned observations is missing, if the data are from a survey, or if historical data are being screened, the arrangement of observations may be quite disorganized. This paper presents a simple method for finding a set of independent normal equations when the arrangement of observations is completely arbitrary. From these normal equations and their solution one can determine estimates of the parameters of the general linear model being fitted to the data, which linear functions of parameters are estimable, which hypotheses are testable, sums of squares for testable hypotheses, and point estimates and confidence intervals for estimable functions. A numerical example is included to illustrate the method.