Open AccessRobustness of T-test Based on Skewness and Kurtosis
Author(s) -
Steven T. Garren,
Kate McGann Osborne
Publication year - 2021
Publication title -
journal of advances in mathematics and computer science
Language(s) - English
Resource type - Journals
ISSN - 2456-9968
DOI - 10.9734/jamcs/2021/v36i230342
Subject(s) - kurtosis , skewness , statistics , mathematics , statistic , percentile , test statistic , shape parameter , sample size determination , type i and type ii errors , normal distribution , statistical hypothesis testing
Coverage probabilities of the two-sided one-sample t-test are simulated for some symmetric and right-skewed distributions. The symmetric distributions analyzed are Normal, Uniform, Laplace, and student-t with 5, 7, and 10 degrees of freedom. The right-skewed distributions analyzed are Exponential and Chi-square with 1, 2, and 3 degrees of freedom. Left-skewed distributions were not analyzed without loss of generality. The coverage probabilities for the symmetric distributions tend to achieve or just barely exceed the nominal values. The coverage probabilities for the skewed distributions tend to be too low, indicating high Type I error rates. Percentiles for the skewness and kurtosis statistics are simulated using Normal data. For sample sizes of 5, 10, 15 and 20 the skewness statistic does an excellent job of detecting non-Normal data, except for Uniform data. The kurtosis statistic also does an excellent job of detecting non-Normal data, including Uniform data. Examined herein are Type I error rates, but not power calculations. We nd that sample skewness is unhelpful when determining whether or not the t-test should be used, but low sample kurtosis is reason to avoid using the t-test.