Validity and Applicability of Several Tests for Comparing Marginal Distributions of a Square Table with Ordered Categories

Abstract

There exist several methods of testing homogeneity of two marginal distributions of a square contingency table with ordinal categories.In the present paper, some notes on the properties of the test are made and validity and powers are examined by Monte Carlo simula tion. A modification of the Koch-Reinfurt test is proposed for achieving better small-sample approximation to the null distribution.Furthermore a cumulative chi-square test is proposed, which is expected to have fairly high power for broad alternatives of location and/or scale shift.Simulation studies indicate that in small or moderate samples, more accurate approxima tion distributions are worth developing for some of the tests examined. It is also shown that the power of tests is highly dependent on the latent distributional model and the skewness of the marginal probabilities.

BMGE (Block Mapping and Gathering with Entropy): a new software for selection of phylogenetic informative regions from multiple sequence alignments

“…another matched-pairs test assessing the complete symmetry inside F ) was tried instead of the Stuart's test in the stationary-based trimming, but it led to worse results in the simulation analysis (not shown). Finally, as stressed in [ 43 ], Stuart's test is based on ordinary χ 2 approximation and is not appropriate for small samples, particularly when the number of categories (i.e. the row number in F ) is not small.…”

“…If these two sequences have similar character state composition, then, for each character state s = 1, 2,..., r , this sequence pair verifies the null hypothesis F s. = F .s , named the marginal homogeneity (e.g. [ 30 , 43 ]) or marginal symmetry (e.g. [ 31 ]).…”