Transformation works for non-normality? On one-sample transformation trimmed t methods

If the assumption of normality is not satisfied, there is no simple solutio n to this problem for the one-sample t test. The present study proposes Hal l's or Johnson's transformation in conjunction with the trimmed mean to dea l with the problem. Computer simulation is carried out to evaluate the smal l-sample behaviour of the proposed methods in terms of Type I error rate an d statistical power. The proposed methods are compared with the conventiona l Student t, Yuen's trimmed t, Johnson's transformation untrimmed t, and Ha ll's transformation untrimmed t statistics for one-sided and two-sided test s. The simulation results indicate that the proposed methods can control Ty pe I error well in very extreme conditions and are more powerful than the c onventional methods.