Normalized Johnson's transformation one-sample trimmed t for non-normality

The present study suggests the use of the normalized Johnson transformation trimmed t statistic in the one-sample case when the assumption of normality is violated. The performance of the proposed method was evaluated by Monte Carlo simulation, and was compared with the conventional Student t statistic, the trimmed t statistic and the normalized Johnson's transformation untrimmed t statistic respectively. The simulated results indicate that the proposed method can control type I error very well and that its power is greater than the other competitors for various conditions of non-normality. The method can be easily computer programmed and provides an alternative for the conventional t test.