A New Transformed T-Test with a Univariate Normal Goodness of Fit

• Activity Number: 613
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Khairul Islam* and Tanweer Shapla
• Companies: Eastern Michigan University and Eastern Michigan University
• Keywords: Two-sample t-test ; Wilcoxon test ; Transformation ; Goodness-of-fit ; Power of the test

Abstract

A new transformed two-sample t-test has been proposed for testing equality of two population means for skewed distributions. The method involves transformations of skewed distributions to normality by means of a univariate normal goodness of fit approach. The performance of the proposed test is compared with untransformed t-test and the non-parametric analogue of t-test via Wilcoxon rank sum test using real-life examples and simulation from skewed distributions with varying values of skewness, empirically. It reveals that the proposed new test is appropriate for estimating the level of significance and is more powerful than the untransformed t-test and the Wilcoxon rank sum test for skewed distributions.