Abstract
It is proposed that statistics for comparing dispersion (i.e., spread, scale; e.g., variance) when data are tied should be tie-centered. For statistics which are score sums, this means that if the highest score (indicating the least difference from a center of the data) is assigned to the. median when there are no ties, then the median should have the highest score when there are ties. Using standard methods for ties, most popular dispersion rank test statistics are not tie-centered, e.g., the Ansari- Bradley, Mood and Siegel-Tukey statistics. A new tie-centered rank test statistic with a Wilcoxon distribution is proposed for ordered categorical data. For data consisting of meaningful point values with many ties, the Fligner- Killeen test is proposed. Exact tests and random cut-points tests can be done with these statistics, and cluster sampling can be accommodated.
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