PROPOSED NONPARAMETRIC TESTS FOR PROPORTION TESTING AND THE MIXED TWO-SAMPLE DESIGN

Abstract

In this research, we propose five new mixed-design tests that consist of a completely randomized design (CRD) and a randomized complete block design (RCBD). The first two proposed nonparametric tests are designed to assess differences in treatment effects based on proportions within a mixed design framework. In contrast, the third, fourth, and fifth tests are developed to test whether the difference between two treatment means is greater than zero. The first proposed test combines Cochran’s Q test for dependent data within the RCBD and the Chi square test for independent data within the CRD. The second proposed test combines an alternative approach of Cochran’s Q test, used for dependent binary data in the RCBD, with the Chi-square test, which is applied to independent data in the CRD. The estimated power of the first proposed test is then compared to the estimated power of second proposed test. A simulation study is conducted using various sample sizes to evaluate the performance of each test under different conditions. The third proposed test integrates the standardized Mann-Whitney test for independent data within the CRD and the standardized Sign test for paired data within the paired design portion. Following the same framework, the fourth proposed test maintains this structure but applies a weight of 2 to the standardized Wilcoxon-Mann-Whitney test in the CRD portion. Similarly, the fifth proposed test combines the standardized Sign test and the standardized Wilcoxon-Mann-Whitney test in the CRD but assigns a weight of 2 to the standardized Sign test in the paired design portion. The performance of these tests is evaluated by comparing their estimated powers to one another and to two existing methods developed for similar mixed-design structures: the Dubnicka test and the Magel and Fu test. Comparisons are conducted through a simulation study under various distributions, considering different sample sizes and location parameter values. The estimated power of each test is examined at a significance level of 0.05 using 10000 iterations. The findings provide insights into the efficiency of the proposed tests for analyzing data in mixed-design settings.