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10. EFFECT OF SAMPLE SIZE ON THE CONSISTENCY OF PAIRED T-TEST, WILCOXON SIGN RANK TEST AND SIGN TEST by I. Muhammad and Y. Zakari Volume 50 (March, 2019 Issue)
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EFFECT OF SAMPLE SIZE ON THE CONSISTENCY OF PAIRED T-TEST, WILCOXON SIGN RANK TEST AND SIGN TEST

I. Muhammad1and Y. Zakari

Department of Statistics, University of Ilorin, Nigeria

Department of Statistics, Ahmadu Bello University, Zaria, Nigeria

Abstract

This paper compare the consistency of the Paired t-test, Sign test and Wilcoxon Sign Rank test procedures on paired samples from related population. These tests are conducted under different scenario whether or not the basic parametric assumptions are met for different sample sizes. Hypothesis testing on equality of means require assumptions to be made about the format of the data to be employed. Random samples were simulated from normal and gamma distributions. The three tests procedures were applied on the simulated data sets at various sample sizes (small, moderate and large) and their Type I error and power of the test were studied in both situations under study. The comparison indicates that, the Wilcoxon signed rank is the most consistent in estimating power for the Gamma distribution. Whereas, the Paired t-test suffices as the most consistent and powerful test followed by the Wilcoxon signed rank and then Sign test when the underlined distribution is Normal. The hypothesized mean difference and sample size affect the power of all the tests significantly.

Keywords: T-test, Sign-test, Wilcoxon Sign Rank, Type I error, Power of a test.

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