# Some properties of measures of disagreement and disorder in paired ordinal data

Sammanfattning: The measures studied in this thesis were a measure of disorder, D, and a measure of the individual part of the disagreement, the measure of relative rank variance, RV, proposed by Svensson in 1993. The measure of disorder is a useful measure of order consistency in paired assessments of scales with a different number of possible values. The measure of relative rank variance is a useful measure in evaluating reliability and for evaluating change in qualitative outcome variables.In Paper I an overview of methods used in the analysis of dependent ordinal data and a comparison of the methods regarding the assumptions, specifications, applicability, and implications for use were made. In Paper II an application, and a comparison of the results of some standard models, tests, and measures to two different research problems were made. The sampling distribution of the measure of disorder was studied both analytically and by a simulation experiment in Paper III. The asymptotic normal distribution was shown by the theory of U-statistics and the simulation experiments for finite sample sizes and various amount of disorder showed that the sampling distribution was approximately normal for sample sizes of about 40 to 60 for moderate sizes of D and for smaller sample sizes for substantial sizes of D. The sampling distribution of the relative rank variance was studied in a simulation experiment in Paper IV. The simulation experiment showed that the sampling distribution was approximately normal for sample sizes of 60-100 for moderate size of RV, and for smaller sample sizes for substantial size of RV. In Paper V a procedure for inference regarding relative rank variances from two or more samples was proposed. Pair-wise comparison by jackknife technique for variance estimation and the use of normal distribution as approximation in inference for parameters in independent samples based on the results in Paper IV were demonstrated. Moreover, an application of Kruskal-Wallis test for independent samples and Friedman’s test for dependent samples were conducted.

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