Statistical tests are at the heart of clinical research, yet many of us have wondered at some point: should I use a parametric or a non-parametric test? The answer is not always straightforward and depends on the nature of the data, the sample size, and the assumptions each test requires. This short overview aims to clarify the key differences and help you choose the right tool for your data
What makes a test “parametric”?
Parametric tests assume that your data follow a known distribution, most commonly the normal (Gaussian) distribution, the familiar bell-shaped curve [1]. They also assume homogeneity of variance and rely on estimating population parameters, such as the mean and standard deviation. Some, such as the classical Student’s t-test and ANOVA, also assume homogeneity of variance, though not all parametric tests share this requirement.
Common examples include the Student’s t-test, ANOVA, and the Pearson correlation coefficient. Because they use all the information in the continuous data, parametric tests tend to have greater statistical power, meaning they are more likely to detect a true effect when one exists, provided their assumptions are met.
When to go non-parametric?
Non-parametric tests, sometimes called “distribution-free” tests, do not require the data to follow a specific distribution [2]. Instead, they typically work with ranks or medians rather than raw values. This makes them particularly useful when:
- The data are not normally distributed, and the sample size is too small for the central limit theorem to apply.
- The outcome is measured on an ordinal scale (e.g., a visual analog scale or pain rated as mild, moderate, severe).
- There are significant outliers that could distort the mean.
Well-known equivalents include the Mann-Whitney U test, the Wilcoxon signed-rank test, and the Kruskal-Wallis test.
How to choose?
A common misconception is that non-parametric tests are always “safer”. While they make fewer assumptions, using a non-parametric test on truly normally distributed data sacrifices statistical power and may result in a failure to detect a real difference [3].
Recent evidence and expert consensus suggest that non-parametric tests might actually be overused in medical research [4]. Parametric tests are often remarkably robust to mild violations of normality, particularly with larger sample sizes. On the flip side, if your data show extreme skewness, non-parametric tests can actually be substantially more powerful than parametric ones.
Practical tips
Before defaulting to a test, always start by exploring your data visually (using histograms or Q-Q plots). You can complement this with formal normality tests (like Shapiro-Wilk) , but remember that these can be overly sensitive in large samples and underpowered in small ones [1,2] (Figure 1).
If your data deviate from normality, consider data transformation (e.g., log transformation) to see if you can safely use a more powerful parametric test before switching to non-parametric methods.
Figure 1. Quick decision algorithm for choosing between parametric and non-parametric tests (diagram realized with Rstudio version 4.4.2 and Microsoft Powerpoint).
Take-home message
Neither parametric nor non-parametric tests are inherently better. The right choice depends on your data. Always start by exploring your data visually, check the underlying assumptions, and choose accordingly. When in doubt, consulting a biostatistician early in your study design can save a lot of trouble later.
References and further reading
- Vetter TR. Fundamentals of Research Data and Variables: The Devil Is in the Details. Anesth Analg. 2017 Oct;125(4):1375-1380.
- le Cessie S, Goeman JJ, Dekkers OM. Who is afraid of non-normal data? Choosing between parametric and non-parametric tests. Eur J Endocrinol. 2020 Feb;182(2):E1-E3.
- Bensken WP, Ho VP, Pieracci FM. Basic Introduction to Statistics in Medicine, Part 2: Comparing Data. Surg Infect (Larchmt). 2021 Aug;22(6):597-603.
- Bridge PD, Sawilowsky SS. Increasing physicians’ awareness of the impact of statistics on research outcomes: comparative power of the t-test and Wilcoxon rank-sum test in small samples applied research. J Clin Epidemiol. 1999;52(3):229–235.
Written by Elvis Hysa, EMEUNET Newsletter Sub-Committee member