Abstract
We propose a new nonparametric test based on the rank difference between the paired sample for testing the equality of the marginal distributions from a bivariate distribution. We also consider a modification of the novel nonparametric test based on the test proposed by Baumgartern, Weiβ, and Schindler (1998). An extensive numerical power comparison for various parametric and nonparametric tests was conducted under a wide range of bivariate distributions for small sample sizes. The two new nonparametric tests have comparable power to the paired t test for the data simulated from bivariate normal distributions, and are generally more powerful than the paired t test and other commonly used nonparametric tests in several important bivariate distributions.
Highlights
Paired data are very common in statistical and medicinal research
We propose a new rank difference (RD) test for paired data based on the rank difference between the paired sample to capture the sample difference
We consider an example and apply the five different tests discussed in this article: 1) the paired t test; 2) the Wilcoxon signed rank (WSR) test; 3) the modification of the Wilcoxon rank sum (MWRS) test; 4) the RD test; and 5) the MBWS test
Summary
Paired data are very common in statistical and medicinal research. A typical example is a clinical trial where subjects are measured prior to a treatment, say for elevated systolic blood pressure, and measured again after the treatment with a drug to lower the blood pressure. The two sample paired t test is a commonly used parametric approach for comparing the means of two distributions. It computes the difference between the two measurements of each subject. The Wilcoxon rank sum test ( known as the Mann-Whitney test) [3] [4] is a nonparametric statistical test for assessing whether the two independent samples are from the same distribution. It may be not be suitable for testing paired data without some modification.
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