A Note an asymptotic Expansion of Spericity Test

Abstract

This research is devoted to study the moment of  the likelihood ratio criterion for sphericity test for one- way multivariate repeated measurements analysis of variance model. Also we obtain the asymptotic expansion and limiting distribution of the test statistic. As practical research, a study has been taken to diagnostics and isolation for kinds of becteria which complain with tissue cultivation for the dates and the study of frustrate affection for three  kinds  of  extractor plant , which are called Rhus coriaria and cinnamomum zeylanicum , the excretes of adhesive for the Bswellia Sp plant and by using four kinds of solvent and two different condense. An experimental has been made for getting measurement for the best reacting extractor plant with the solvent by using different affection on frustrate core . Key words: One-Way Multivariate Repeated Measures Model, Sphericity test, Asymptotic Expansion,  MANOVA