AN INTRODUCTION TO SOME NON-PARAMETRIC GENERALIZATIONS OF ANALYSIS OF VARIANCE AND MULTIVARIATE ANALYSIS

摘要: It is clear that a p-variate body of data arranged in q-way classification will formally look llke (p+q)-dimensional contingency table, but distinction can be made between 'variate' and ‘way classification’ along the direction marginal frequencies are supposed to stochastic variates while 'way classification' fixed. When, certain directions, marginals fixed, an approach based on conditional probability argument has been used. In present paper (i) abandoned we start either from single multinomial distribution or product appropriate number different distributions according as, with multi-way frequency data, all ways 'variates' some 'ways classification'. (ii) Also hypotheses posed kinds altogether as have 'multivariate analysis' situation 'analysis variance' situation. The meaningful for one would not too other vice versa. Since abandoned, mathematical theorems which appeal two stated proved by Cramer (1946, chapter 30) such same way which, them, take care discussed this paper. When analogous those usual multivariate analysis, when analysis variance. general methods arose out attempt analyse large mass categorical data. carried out, few typical cases (together numerical analysis) illustrating parts theoretical development presented subsequent only large-sample tests considered. How 'large' sample size validity use these asymptotic techniques, words, results nature approximation involved also later