Robustness of the Yuen <i>t</i> -test in small-sample situations with violations of normality

The purpose of this study is to examine the robustness of the Yuen test in controlling Type I error rates under extreme conditions that frequently arise in applied science research.An analysis of variance (ANOVA) was conducted using four factors: population distribution, total sample size, differences in sample size between groups, and heteroscedasticity between groups.The results showed that the actual Type I error rate of the Yuen test tended to decrease under long-tailed distributions and small sample conditions.Moreover, greater imbalance in group sample sizes was associated with smaller Type I error rates in non-normal conditions.When the assumption of homogeneity of variances was violated, the Type I error rate varied depending on the combination of total sample size and group sample sizes.The findings indicate that the Yuen test was more affected by total and group sample sizes than by distribution shape or variance equality.Therefore, it is recommended to use the t-test when the assumption of homogeneity of variances is satisfied, and to use the Welch test when sample sizes are very small to avoid sample loss due to trimming.