Qualitative Data And Statistical Analysis Of Contingency Tables

Abstract Statistical analysis of qualitative datas, which has been applied in medicine,biology, industry—agriculture and social science, is more and more emphasized recently.Mathematical statistics datas are often classified four classes that include metrical, numerical,ordered and nominal. Metrical and numerical are called quantitative and their statisticalanalysis pertains to distributions of continuous random variables and discrete randomvariables. Ordered and nominal are called qualitative and their statistical analysis pertains tocategorical statistics. Owing to categorical datas are often displayed by contingency tables,analysis of contingency tables is the principal content in statistical analysis of qualitativedatas.This paper solves problems of hierachical Bayes estimators and pesudo－Bayes estimatorsof the probability distributions of qualitative datas. These products extend and improve Bayesestimators. It is important to retain the measure of association between variables oncollapsing or amalgating multidimensional contingency tables. We find necessary andsufficient conditions of simply and strong collapsing. We also study how the amalgamationparadox can be avoided by suitable designs of the sampling experiments and the conditions forthe "homo geneity"of two subpopulations with respect to coefficient of association. At last,we discuss contingency tables containing ordered variables. The paper mainly containsfollowing three parts:I Nonparametric estimation of the probability distributions of qualitative datas isstudied. Under the hierachical prior by the name of mixed Dirichlet distributions, hierachicalBayes estimators is deduced. As well as, pesudo－Bayes estimators is given when risk'. 3.function value get its minimum under squard error loss function.H We study necessary and sufficient conditions fOr simply and strong collapsing I x J xK tables under the interaction and odds ratio. In addition to, we consider amalgamation oftwo -- by -- two contingency tables.ili We summary several elementary methods to analyze contingency tables containingordered variables and show their merit and feasibility by some cases.