A nonparametric test is any statistical procedure where no assumptions are made regarding the distribution of data. The most common types of nonparametric tests include:
- Kruskal-Wallis Test
- Mann Whitney U Test
- Wilcoxon Signed Ranks Test
- Friedman's Test
Before we talk about the Nonparametric Tests, let's understand what Parametric Tests are.
Parametric Tests:
These are hypothesis tests that assume that the data being analyzed follows a distribution (generally Normal Distribution).
Examples of Parametric Tests:
- One Sample z-Test
- Two Sample z-Test
- One Sample t-Test
- Two Sample t-Test
- Paired t-Test
- etc.
Nonparametric Tests:
A nonparametric test does not assume anything about the underlying distribution. That way, these tests can be used on any set of data without any condition.
But then why don't we always use Nonparametric Tests?
Since nonparametric tests do not assume any probability distribution, nonparametric tests' power is lower than the power of parametric tests. Moreover, there may be situations in which you need to make an assumption about the underlying distribution and therefore it makes sense to choose one over another depending upon your situation.
Reasons to Use Nonparametric Tests
Nonparametric tests have several advantages over parametric tests:
1) They don’t assume any specific distributions on the data; hence, they work well with skewed data.
2) The results obtained from them are more robust than those obtained by using parametric tests because they are less sensitive to outliers.
3) Their calculations are much faster compared to the ones performed by parametric tests.
Parametric vs Nonparametric Tests for Mean and Median
Parametric tests (for mean) | Nonparametric tests (for median) |
1-sample z test 1-sample t-test | 1-sample Sign, 1-sample Wilcoxon Signed Rank test |
2-sample t-test | Mann-Whitney test |
One-Way ANOVA | Kruskal-Wallis test Mood’s median test |
Two-way ANOVA | Friedman test |