Covariates In One –Way Multivariate Repeated Measurements Analysis Of Covariance (Ancova) Model

Abstract

One-Way Multivariate Repeated Measures Model,Wilks distribution, Wishart distribution,(ANCOVA) analysis of covariance , covariates.This research is devoted to the study theOne -Way Multivariate repeated measurements analysis of covariance model (MRM ANCOVA), which contains one between-units factor (Group with q levels) incorporating one random effect, one within-units factor كرّرَ Multivariate الأحادي الإتجاه الإجراءات تُشكّلُ، توزيع Wilks، توزيع Wishart، (Ancova) تحليل التغايرِ , covariates. (Time with p levels) and two covariates ( , ). For this model the covariates are time-independent, that is measured only once. The test statistics of various hypotheses on between-unites factor, within-units factor and the interaction between them are given, and including the application to study the assessment of water quality of the northern part of shatt AL-Arab river at Basra,Iraq and determine its suitability for aquatic environment ,drinking and irrigation, through studying some variables including the chemical ,physical and biological quality variables that have the greatest effect on water quality in order to find the index of water quality,which is available in the experiment during one year through twelve months.