A Study of Efficiency of Parametric and Nonparametric Statistics in Testing of Central Difference between Two Populations

Abstract

This research aimed to study the efficiency of parametric and nonparametric statistics in testing of central difference between two populations. The test statistics used to study the efficiency were t test, Mann Whitney U test, Van der Waerden test, Wald Wolfowitz Runs test and Modified U test. Classification of the population according to normal distribution, negative skewness and leptokurtic kurtosis distribution and positive skewness and leptokurtic kurtosis distribution. The sample sizes of two population were (5,5), (5,10), a small sample representative, (20,20), (25,20), a medium sample representative, and (50,50), (50,100), a large sample representative. The ratios of variance were (1:1) and (1:2) at a significant level of 0.05. The criteria used to compare the efficiency were the ability to control the type I error and power of the test. The results showed that: When the population has normal distribution, The test statistics have the highest power of the test and to control the type I error for small sample sizes were t test and Van der Waerden test, for medium and large sample sizes were Modified U test. When the population has negative skewness and leptokurtic kurtosis distribution, The test statistics have the highest power of the test and to control the type I error for small sample sizes were t test and Van der Waerden test, for medium and large sample sizes were Mann Whitney U test. When the population has positive skewness and leptokurtic kurtosis distribution, The test statistics have the highest power of the test and to control the type I error for small sample sizes were t test and Van der Waerden test, for medium sample sizes were Mann Whitney U test and for large sample sizes were t test and Mann Whitney U test.