Parametric vs Nonparametric Tests

Parametric tests assume the data follow a particular distribution (often normal) and use parameters such as the mean and SD; nonparametric tests make fewer distributional assumptions, usually working with ranks. Choose by the data type, distribution, sample size and design, and decide the plan in advance.

Common pairs

Trade-offs

• Parametric tests are more efficient when assumptions hold.
• Nonparametric tests are more robust to skew and outliers and suit ordinal data, but may have less power when data are truly normal and they test a different hypothesis (about ranks or distributions, not strictly means).
• With large samples, parametric tests are often robust to moderate non-normality because of the central limit theorem, but severe skew or outliers still matter.

How to decide

1. Identify the data type: ordinal data usually require nonparametric methods.
2. Look at the distribution (histogram, plots) rather than relying only on a normality test, which is unreliable with very small or very large samples.
3. Consider transformations (for example log) for skewed data.
4. Pre-specify the main analysis, and check robustness with the alternative.

Illustrative example

Invented for teaching. Length of stay (days) is highly right-skewed in two groups of 30 patients. The authors plan a Mann-Whitney test and report medians (IQR). They also report a bootstrap confidence interval for the difference in medians, as advised by a statistician.

Common pitfalls

• Choosing the test after seeing which gives p < 0.05.
• Using the normality test p-value alone to choose.

Key takeaways

• Choose a test that fits the data and question; pre-specify it.
• Report summary statistics that match the test.

This page is general educational information about research methods. It is not medical, legal or regulatory advice; follow your institution's ethics board and your target journal's instructions.