t-tests, non-parametric tests, and large studies—a paradox of statistical practice?

A simulation study is used to compare the rejection rates of the Wilcoxon-Mann-Whitney (WMW) test and the two-sample t-test for increasing sample size. Samples are drawn from skewed distributions with equal means and medians but with a small difference in spread. A hypothetical case study is used for illustration and motivation.The WMW test produces, on average, smaller p-values than the t-test. This discrepancy increases with increasing sample size, skewness, and difference in spread. For heavily skewed data, the proportion of p<0.05 with the WMW test can be greater than 90% if the standard deviations differ by 10% and the number of observations is 1000 in each group. The high rejection rates of the WMW test should be interpreted as the power to detect that the probability that a random sample from one of the distributions is less than a random sample from the other distribution is greater than 50%.Non-parametric tests are most useful for small studies. Using non-parametric tests in large studies may provide answers to the wrong question, thus confusing readers. For studies with a large sample size, t-tests and their corresponding confidence intervals can and should be used even for heavily skewed data.