Comparison of the Statistical Power of Siegel-Tukey and Savage Tests: A Study with Monte Carlo Simulation

This study presents the results of a Monte Carlo simulation to compare the statistical power of Siegel-Tukey and Savage tests.The main purpose of the study is to evaluate the statistical power of both tests in scenarios involving Normal, Platykurtic and Skewed distributions over different sample sizes and standard deviation values.In the study, standard deviation ratios were set as 2, 3, 4, 1/2, 1/3 and 1/4 and power comparisons were made between small and large sample sizes.For equal sample sizes, small sample sizes of 5, 8, 10, 12, 16 and 20 and large sample sizes of 25, 50, 75 and 100 were used.For different sample sizes, the combinations of (4, 16), (8, 16), (10, 20), (16, 4), (16, 8) and (20, 10) small sample sizes and (10, 30), (30, 10), (50, 75), (50, 100), (75, 50), (75, 100), (100, 50) and (100, 75) large sample sizes were examined in detail.According to the findings, the power analysis under variance heterogeneity conditions shows that the Siegel-Tukey test has a higher statistical power than the other nonparametric Savage test at small and large sample sizes.In particular, the Siegel-Tukey test was reported to offer higher precision and power under variance heterogeneity, regardless of having equal or different sample sizes.