Parametric and non-parametric tests

If you want to calculate a hypothesis test, you must first check the prerequisites of the hypothesis test. A very common requirement is that the data used must be subject to some distribution, usually the normal distribution. If your data are normally distributed, parametric tests can usually be used, if they are not normally distributed, non-parametric tests are usually used.

Parametric tests

If the data are normally distributed, parametric tests such as the t-test, ANOVA or Pearson correlation are used.

Non-parametric tests

If the data are not normally distributed, the nonparametric tests are used. These are for example the Mann-Whitney U-Test or the Wilcoxon-Test.

Nonparametric tests are therefore used when the scale level is not metric, the true distribution of the random variables is not known, or the sample is simply too small to assume a normal distribution. To assume a normal distribution, the sample should at least be larger than 30 cases.

Thus, non-parametric tests are more robust than parametric tests and can be calculated in significantly more situations. Parametric tests, however, have a greater statistical power than the non-parametric tests. Therefore, if the assumptions for a parametric test are met, it should always be used.

The following table lists the most common parametric and nonparametric tests. Depending on the number of samples and whether they are dependent or independent, there is a parametric and a nonparametric test.

Parametric tests Nonparametric tests
One sample Simple t-Test Wilcoxon test for one sample
Two dependent samples Paired Sample t-Test Wilcoxon-Test
Two independent samples Unpaired Sample t-Test Mann-Whitney U-Test
More than two independent samples One-way ANOVA Kruskal-Wallis-Test
More than two dependent samples Repeated Measures ANOVA Friedman-Test
Correlation between two variables Pearson Correlation Spearman-Correlation

If you use DATAtab, you can have the prerequisites for your hypothesis test checked, if the prerequisites are not met, simply make the selection of "Nonparametric test", then the non-parametric counterpart will be calculated automatically.

Here you will learn how to check your data for normal distribution.

Calculate parametric and non-parametric test procedures

Parametric and non-parametric tests can be calculated directly online here on DATAtab, just visit the Hypothesis Test Calculator and select the variables you want to study. Then you can choose whether you want to calculate a parametric test or a non-parametric test.

Cite DATAtab: DATAtab Team (2024). DATAtab: Online Statistics Calculator. DATAtab e.U. Graz, Austria. URL https://datatab.net