Johnsons transformation two-sample trimmed t and its bootstrap method for heterogeneity and non-normality

The present study investigates the performance of Johnsonʹs transformation trimmed t statistic, Welchʹs t test, Yuenʹs trimmed t, Johnsonʹs transformation untrimmed t test, and the corresponding bootstrap methods for the two-sample case with small/unequal sample sizes when the distribution is non-normal and variances are heterogeneous. The Monte Carlo simulation is conducted in two-sided as well as one-sided tests. When the variance is proportional to the sample size, Yuenʹs trimmed t is as good as Johnsonʹs transformation trimmed t. However, when the variance is disproportional to the sample size, the bootstrap Yuenʹs trimmed t and the bootstrap Johnsonʹs transformation trimmed t are recommended in one-sided tests. For two-sided tests, Johnsonʹs transformation trimmed t is not only valid but also powerful in comparison to the bootstrap methods.