Testing the equality of two ordered multinomial proportions

来源 :IMS-China International Conference on Statistics and Probabi | 被引量 : 0次 | 上传用户:einstein_2
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  This article considers the problem of testing the equality of two multinomial proportions from ordered categories.The proportional odds model is adopted to reflect the order among categories and it expresses the difference between the two multinomial distributions via a single location-type parameter.As a result, the problem of interest is reduced to the problem of testing the location-type parameter being zero for all possible collapsed 2×2 tables.Score, five different Wald-type and likelihood ratio statistics are first derived to test if the location-type parameter equals zero for any particular collapsed 2×2 table.Different multiple comparison procedures (i.e., namely, the Bonferroni, Simes, Hochberg, siugle-step adjusted P-value MaxT, single-step adjusted P-value MinP, and step-down adjusted P-value procedures) are then proposed to implement the developed statistics for testing if the location-type parameter cquals to zero for all possible collapsed 2×2 tables.Simulation studies arc conducted to compare the performance of our methods with the asymptotic and bootstrap Wilcoxon midrank tests.Amongst, score test based on the single-step adjusted p-value MinP and step-down adjusted p-value procedures are recommended for they can well control their type I error rates at around the pre-specified nominal level while they yield reasonably high powers.We illustrate our methods with two real examples.
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