Two-sample Location Tests under Violation of the Normality and Variance Homogeneity Assumptions
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Abstract
In this research, the performance of four test statistics, the independent t-test, Welch’s t-test, the Mann-Whitney test and the permutation test, were compared under combined violations of normality and homogeneity of variance. In a simulation study, we generated data from symmetric and asymmetric distributions. The results showed that all methods displayed reliable results in terms of protecting type I error rates at the nominal level, except for the Mann-Whitney test which provides an inflation of type I error rates. Considering the power of the tests for symmetric distributions with the homogeneity of variances, the independent t-test is the best test when the sample data are drawn from normal and uniform distributions, while the Mann-Whitney test is the most powerful for the logistic and Laplace distributions. With symmetric distributions in heterogeneity of variance cases, the permutation test is the most powerful test. For gamma distribution, the permutation test is the best test. In addition, this test is also the best option for the low degree of skewness for Log-normal distribution.
Keywords: permutation test; Welch’s t-test; Mann-Whitney test; statistical power; type I error
*Corresponding author: E-mail: bumrungsak@buu.ac.th
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References
Boneau, C.A., 1960. The effects of violations of assumptions underlying the t test. Psychological Bulletin, 57(1), 49-64.
Fagerland, M.W. and Sandvik L., 2009. Performance of five two-sample location tests for skewed distributions with unequal variances. Contemporary Clinical Trials, 30, 490-496.
Nadim, N., 2008. The Mann‐Whitney U: a test for assessing whether two independent samples come from the same distribution. Tutorials in Quantitative Methods for Psychology, 4(1), 13-20.
Ernst, M.D., 2004. Permutation methods: a basis for exact inference. Statistical Science, 19(4), 676-685.
R Development Core Team, 2019. R: A Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing.
Hatchavanich, D., 2014. A comparison of type I error and power of Bartlatt’s test, Levene’s test and O’Brien’s test for homogeneity of variance test. Southeast-Asian Journal of Sciences, 3(2), 181-194.
Kasuya, E., 2001. Mann-Whitney U test when variances are unequal. Animal Behaviour, 61, 1247-1249.
Stonehouse, J.M. and Forrester, G.J., 1998. Robustness of the t and U tests under combined assumption violations. Journal of Applied Statistics, 25(1), 63-74.
Fagerland, M.W., 2012. t-tests, non-parametric tests, and large studies-a paradox of statistical practice? BMC Medical Research Methodology, 12, 78, https://doi.org/10.1186/1471-2288-12-78.