A batractlSummaryThis paper considers a common problem in analysis of variance where the responses to a set of treatments are nominal (i.e. are recorded in frequencies) with no underlying metric. Reasoning by analogy from standard analysis of variance of a two-way classification we develop chi-square tests for significance of treatments and interactions. Two tests are proposed for interaction and their asymptotic properties are studied.

k nij = niik, Var (nip) = nijpiik. ; k =k k ' k JKE B. ONUKOQU Two methode of testing multivariate hypotheses in an I x J x K contingency table are presented. In one case, use is made of the trace of the matrix of sum of squares and sum of products while in the other, determinants of the matrices are used to construct test statistics. Asymptotic equivalence of the methods ia shown.

AbetraetThis paper shows that categorical data can be analysed by analysis of variance methods; applying least squares, linear additive models, P-testa for significance and so forth. It enriches an alternative analysis which leads to chi-square tests, c.f. author (1982), LIQHT and MARQOLIN (1971).

Results are obtained showing that when a response surface can be modelled as a single function, then a single regressor is more efficient and less biased than a segmented regression. However, if the surface is segmented, a segmented regressor is less biased than a single regressor. Areas of application are indicated.

The paper develops F -tests with single numerator degree of freedom (d.L) for interaction in a twoway crossed classification with one observation per cell. Thus, a convenient and possibly more powerful alternative to the JOHNSON and GRAYBILL (1972) test is provided.