Parametric and non-parametric tests

What are parametric and non-parametric tests?

If you want to calculate a hypothesis test, you must first check the assumptions 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.

Central Limit Theorem

The Central Limit Theorem states that the sampling distribution of the mean approaches normality as sample size increases. To assume a normal distribution, the sample should consist of more than 30 cases.

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. 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 be used.

Note: Normality is only one of several assumptions, and it is important to check all assumptions of the respective test. For more details about that, please have a look at our specific tutorials on e.g. t-tests or ANOVA.

Overview of parametric and non-parametric tests

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

Calculate parametric and non-parametric tests with numiqo

Parametric and non-parametric tests can be calculated directly online here on numiqo.com, 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.

Using numiqo, you can also have the assumptions for your hypothesis test checked, if the assumptions 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.