Karesel Olumsallık Tablolarında Düzey Ayırt Edilebilirliği ve Uyum

Abstract

In square contingency tables, analysis of agreement between the row and column classifications is of interest. For nominal categories, kappa coefficient is used to summarize the degree of agreement between two raters. For ordinal categories, weighted kappa coefficient is used instead of kappa coefficient. Numerous extensions and generalizations of kappa and weighted kappa statistics have been proposed in the literature. In addition to investigate the agreement between raters for square contingency tables, the category distinguishability should be considered. The kappa coefficient is insufficient to measure the category distinguishability. In that case, the degree of distinguishability which is a measure of the ability of the raters to distinguish the categories is suggested to use. In practice, some problems have occurred with regards to the use of the degree of distinguishability. The degrees of distinguishability have been found negative in some tables. Furthermore, there is not any information about how to interpret the degree of distinguishability except the general one. This aim of this study is to focus on agreement coefficient and degree of distinguishability in square contingency tables together. In this thesis, the corrected degree of distinguishability and average degree of distinguishability are suggested to solve the problem of calculating the degree of distinguishability outside the defined range. Furthermore, it is also aimed to determine the interpretation levels for the degree of distinguishability. A simulation study is performed to compare the proposed corrected degree of distinguishabilities and the classical degree of distinguishabilities and the results are discussed over numerical examples.