Non-Parametric Tests

“Do not judge a book by its cover,” as the old saying goes. Data can often be deceptive and is not always complicit with our assumptions. Like books with terrible covers or misleading summaries, your dependent variable might be more complicated than it looks.

Many types of data and variables do not adhere to the normal distribution. That means using parametric tests will give us misleading answers. The distribution of the variable in the population does not fit our preconceived notion of normality. It means we need to find a different way to test the null hypothesis.

Luckily, you already know a few of these tests! Here, we will review what exactly they do and how to use them.


Chi-Square Hypothesis Testing

The Chi-Square method lets you assess multiple categorical variables. It can also help you determine if your experimental observations adhere to a theoretical model. But the Chi-Square Test does not require your data to be normally distributed. The Chi-Square is useful if your dataset includes coin tosses, biological sex and other measurements of categorical frequency.


Spearman Correlation

This relationship measure does not identify differences between two groups. However, it can map out the relationships between any ordinal/continuous variables. This test ranks all of your data by its valued rank, for example if the highest value was ten, it would be ranked first.

Then the Spearman Correlation will look at how well two ranked variables correlate with each other. The Coefficient of Correlation will tell you how well these two variables describe each other.


ANOVA Alternatives

For many different comparisons, psychologists will likely use ANOVAs. While they are robust statistical tests, they do not work well with non-parametric data. Here, there are two alternatives depending on the type of data and comparisons you are making.

The Mann-Whitney test is a ranked version of a One-Way or Two-Way ANOVA. When we are measuring the differences between two different groups, this test will rank the dependent variables to see if they are randomly distributed. You will then receive a P-value that tells you whether or not to reject your null hypothesis. See the table below for an example of “ranking” different measurements and values.

The Wilcoxon-Signed Rank Test is a non-parametric version of repeated-measures or mixed ANOVAs. It takes into account the differences within samples. It uses a similar ranking approach in order to assess whether there is a change across the repeated measures.



Non-parametric tests are helpful when you realize your data or traits are not normally distributed. While they also work on normally distributed data, they have less power to reject a null hypothesis. That means running a normally distributed dataset through a non-parametric test would likely yield a higher P-value. To summarize:

  1. The Chi-Square test is a non-parametric test for categorical data
  2. Spearman correlation is a non-parametric relationship test; an alternative for Pearson correlation
  3. Mann-Whitney U Test is an alternative for any ANOVA looking between different groups
  4. Wilcoxon Ranked Sum Test is an alternative for repeated measure ANOVA tests