Type I Error and Power Rates of T1 Statistic

The effects of nonnormality and heteroscedasticity on the T1 test statistic was investigated using two methods of trimming namely the proposed automatic trimmed mean and the typical fixed amount of trimming. These are typical problems in any test of equality of central tendency measure. For the test statistic, three automatic trimming procedures using different scale estimators MADn, Tn, and LMSn, and a fixed trimmed mean procedure were examined for their robustness via Type I error and power rates. To identify the robustness of each procedure, several variables were manipulated such as number of groups, balanced and unbalanced sample sizes, variance heterogeneity, pairing of group variances and group sample sizes, and types of distributions. The findings show that when the distribution is normal-tailed with heterogeneous variances, the T1 statistic with automatic trimming using Tn performed reasonably well. With regard to power, the automatic trimming is able to produce high power rates especially for the conditions of unequal sample sizes and homogeneous variances.