Nonparametric tests don’t require that your data follow the normal distribution. They’re also known as distribution-free tests and can provide benefits in certain situations. Typically, people who perform statistical hypothesis tests are more comfortable with parametric tests than nonparametric tests.
You’ve probably heard it’s best to use nonparametric tests if your data are not normally distributed—or something along these lines. That seems like an easy way to choose, but there’s more to the decision than that.
In this post, I’ll compare the advantages and disadvantages to help you decide between using the following types of statistical hypothesis tests:
- Parametric analyses to assess group means
- Nonparametric analyses to assess group medians
In particular, I’d like you to focus on one key reason to perform a nonparametric test that doesn’t get the attention it deserves! If you need a primer on the basics, read my hypothesis testing overview.
Related Pairs of Parametric and Nonparametric Tests
Nonparametric tests are a shadow world of parametric tests. In the table below, I show linked pairs of statistical hypothesis tests.
|Parametric tests of means||Nonparametric tests of medians|
|1-sample t-test||1-sample Sign, 1-sample Wilcoxon|
|2-sample t-test||Mann-Whitney test|
|One-Way ANOVA||Kruskal-Wallis, Mood’s median test|
|Factorial DOE with a factor and a blocking variable||Friedman test|
Advantages of Parametric Tests
Advantage 1: Parametric tests can provide trustworthy results with distributions that are skewed and nonnormal
Many people aren’t aware of this fact, but parametric analyses can produce reliable results even when your continuous data are nonnormally distributed. You just have to be sure that your sample size meets the requirements for each analysis in the table below. Simulation studies have identified these requirements. Read here for more information about these studies.
|Parametric analyses||Sample size requirements for nonnormal data|
|1-sample t-test||Greater than 20|
|2-sample t-test||Each group should have more than 15 observations|
You can use these parametric tests with nonnormally distributed data thanks to the central limit theorem. For more information about it, read my post: Central Limit Theorem Explained.
Advantage 2: Parametric tests can provide trustworthy results when the groups have different amounts of variability
It’s true that nonparametric tests don’t require data that are normally distributed. However, nonparametric tests have the disadvantage of an additional requirement that can be very hard to satisfy. The groups in a nonparametric analysis typically must all have the same variability (dispersion). Nonparametric analyses might not provide accurate results when variability differs between groups.
Conversely, parametric analyses, like the 2-sample t-test or one-way ANOVA, allow you to analyze groups that have unequal variances. In most statistical software, it’s as easy as checking the correct box! You don’t have to worry about groups having different amounts of variability when you use a parametric analysis.
Related post: Measures of Variability
Advantage 3: Parametric tests have greater statistical power
Related post: Statistical Power and Sample Size
Advantages of Nonparametric Tests
Advantage 1: Nonparametric tests assess the median which can be better for some study areas
Now we’re coming to my preferred reason for when to use a nonparametric test. The one that practitioners don’t discuss frequently enough!
For some datasets, nonparametric analyses provide an advantage because they assess the median rather than the mean. The mean is not always the better measure of central tendency for a sample. Even though you can perform a valid parametric analysis on skewed data, that doesn’t necessarily equate to being the better method. Let me explain using the distribution of salaries.
Salaries tend to be a right-skewed distribution. The majority of wages cluster around the median, which is the point where half are above and half are below. However, there is a long tail that stretches into the higher salary ranges. This long tail pulls the mean far away from the central median value. The two distributions are typical for salary distributions.
In these distributions, if several very high-income individuals join the sample, the mean increases by a significant amount despite the fact that incomes for most people don’t change. They still cluster around the median.
In this situation, parametric and nonparametric test results can give you different results, and they both can be correct! For the two distributions, if you draw a large random sample from each population, the difference between the means is statistically significant. Despite this, the difference between the medians is not statistically significant. Here’s how this works.
For skewed distributions, changes in the tail affect the mean substantially. Parametric tests can detect this mean change. Conversely, the median is relatively unaffected, and a nonparametric analysis can legitimately indicate that the median has not changed significantly.
You need to decide whether the mean or median is best for your study and which type of difference is more important to detect.
Advantage 2: Nonparametric tests are valid when our sample size is small and your data are potentially nonnormal
Use a nonparametric test when your sample size isn’t large enough to satisfy the requirements in the table above and you’re not sure that your data follow the normal distribution. With small sample sizes, be aware that tests for normality can have insufficient power to produce useful results.
This situation is difficult. Nonparametric analyses tend to have lower power at the outset, and a small sample size only exacerbates that problem.
Advantage 3: Nonparametric tests can analyze ordinal data, ranked data, and outliers
Parametric tests can analyze only continuous data and the findings can be overly affected by outliers. Conversely, nonparametric tests can also analyze ordinal and ranked data, and not be tripped up by outliers.
Sometimes you can legitimately remove outliers from your dataset if they represent unusual conditions. However, sometimes outliers are a genuine part of the distribution for a study area, and you should not remove them.
You should verify the assumptions for nonparametric analyses because the various tests can analyze different types of data and have differing abilities to handle outliers.
If your data use the ordinal Likert scale and you want to compare two groups, read my post about which analysis you should use to analyze Likert data.
Related post: Data Types and How to Use Them
Advantages and Disadvantages of Parametric and Nonparametric Tests
Many people believe that the decision between using parametric or nonparametric tests depends on whether your data are normally distributed. If you have a small dataset, the distribution can be a deciding factor. However, in many cases, this issue is not the critical issue because of the following:
- Parametric analyses can analyze nonnormal distributions for many datasets.
- Nonparametric analyses have other firm assumptions that can be harder to meet.
The answer is often contingent upon whether the mean or median is a better measure of central tendency for the distribution of your data.
- If the mean is a better measure and you have a sufficiently large sample size, a parametric test usually is the better, more powerful choice.
- If the median is a better measure, consider a nonparametric test regardless of your sample size.
Lastly, if your sample size is tiny, you might be forced to use a nonparametric test. It would make me ecstatic if you collect a larger sample for your next study! As the table shows, the sample size requirements aren’t too large. If you have a small sample and need to use a less powerful nonparametric analysis, it doubly lowers the chance of detecting an effect.