# Robustness of Alternative and Classical Statistics in Two-sample Location Tests for Small Sample Sizes

## Keywords:

two-sample location tests, small sample sizes, bootstrap test, permutation test, parametric test, nonparametric test, robustness## Abstract

When the sample size is small, there is a possibility that the two population groups do not follow assumptions. This includes population distribution and variance. Thus, proper statistical techniques must be selected for generalisation. This article classifies statistical techniques into two types: First, classical statistics consisting of independent t-test, Welch t-test, and exact Wilcoxon-Mann-Whitney test (WMW) and, second, alternative statistics consisting of nonparametric bootstrap t-test (NBTT), nonparametric bootstrap Welch t-test (NBWT), nonparametric bootstrap Welch test based on rank (NBWR), and an exact permutation t-test (PTT). The objective of this study was to propose an alternative statistical method for a small sample size study. The data simulation tested both normal and non-normal distributions including equal and unequal variances. The results revealed that when the populations had normal or non-normal distribution and equal variances, almost all test statistics had robustness at a significance level of 0.05. For a significance level of 0.01, if at least one group had normal distribution, the Welch t-test was the most robust. If there were other distributions, the independent t-test was most robust. For unequal variance, when at least one group had a normal distribution with higher variance than other groups, the Welch t-test could control type I errors in all conditions at significance levels of 0.05 and 0.01. In other cases, it was non-robust. Therefore, if a small sample size is applied, the results must be carefully generalized.

**Keywords:** two-sample location tests, small sample sizes, bootstrap test, permutation test, parametric test, nonparametric test, robustness

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