Statistics: What are Parametric & Nonparametric Statistical Tests?

Introduction

Let’s say you want to figure out if men are taller than women. In order to do this you will have to use a hypothesis test but which hypothesis test will you use, parametric or nonparametric tests? What are parametric and nonparametric tests? What’s the difference? Well in today’s article we will briefly cover that.

What are they?

Well if you want to compute a hypothesis test you must first check for the assumptions. One of the most common assumptions is that data must show a certain type of distribution(often a normal distribution) in order to perform a certain type of test. This is what differentiates parametric tests from non-parametric tests. Parametric tests are types of tests used when the data is normally distributed and non-parametric tests are used when the data is not normally distributed. Non-parametric tests are often used when dealing with categorical or ordinal data. What about the other assumptions? For the individual test you have to check for further assumptions but in general there are less assumptions for non-parametric tests as there are for parametric tests. But then why do we need parametric tests? Well parametric tests are more powerful than nonparametric tests. What does that mean though? Well let’s explain that through an example! Let’s say you have formulated your null hypothesis which is that the height of men and women do not differ. Whether the null hypothesis is rejected depends on the difference in salary along with the difference in sample size. In a parametric test a smaller difference in height or a smaller sample size is enough to reject the null hypothesis. If possible, always use parametric tests! Parametric tests provide more precise estimates if assumptions are satisfied.

Common Tests

I want to finish off this article by showing different parametric tests and their corresponding non-parametric tests.

| Type of Sample            | Parametric Test            | Non-Parametric Test               |
|---------------------------|----------------------------|-----------------------------------|
| One Sample                | One-sample t-test          | Wilcoxon signed-rank test         |
| Two Independent Samples    | Independent t-test         | Mann-Whitney U test               |
| Two Dependent Samples      | Paired t-test              | Wilcoxon signed-rank test         |
| Multiple Independent Samples | Analysis of Variance (ANOVA) | Kruskal-Wallis test             |
| Multiple Dependent Samples   | Repeated Measures ANOVA    | Friedman test                    |