Who is afraid of non-normal data? Choosing between parametric and non-parametric tests: a response

Extract

We read with great interest the Methodology Editorial on ‘Choosing between parametric and non-parametric tests’ by le Cessie et al. in the Journal (1). The topic is of wide interest to readers given that this is a frequent issue clinical researchers face in their daily work. The authors argue that the use of a t-test is preferable over non-parametric tests, as it does not necessarily require the data to be normally distributed, working well for moderately skewed distributions. They invoke the central limit theorem, which proves that the statistical mean in a larger sample (n > 25–50) is robustly independent of the normal distribution.

The question arises as to whether clinicians should be mainly interested in central tendency. We present an example for TSH where use of the t-test could be favoured following these recommendations despite the physiologically known non-normal distribution of the hormone (1). Two large clinical samples are compared – using some data from a previous prospective study (2) – a control group (n = 271) where any contamination with thyroid autoimmune disease was carefully excluded and a test sample (n = 251), which included untreated euthyroid (TSH within the reference range) subjects that tested positive for thyroid peroxidase antibodies (TPO Ab). TSH distribution in the samples is non-normal (Fig. 1A). The contamination of the test sample with autoimmune diseases is apparent in Fig. 1. Performing both parametric and non-parametric between-group tests returns the following statistical results, unpaired Welch t-test: mean difference 0.12 mIU/L (95%CI: −0.04, 0.28), P = 0.15 and Wilcoxon rank-sum test: W = 30,059, P = 0.02, using the R statistical package (version 3.6.2 for Mac (3)). The visibly observed difference between the two groups in these data is correctly indicated by Wilcoxon test, but not by the t-test.