# Assumptions of the Mann-Whitney U test

In order to run a Mann-Whitney U test, the following four assumptions must be met. The first three relate to your choice of study design, whilst the fourth reflects the nature of your data:

- Assumption #1: You have
**one dependent variable**that is measured at the**continuous**or**ordinal**level. Examples of**continuous variables**include revision time (measured in hours), intelligence (measured using IQ score), exam performance (measured from 0 to 100), weight (measured in kg), and so forth. Examples of**ordinal variables**include Likert items (e.g., a 7-point scale from "strongly agree" through to "strongly disagree"), amongst other ways of ranking categories (e.g., a 5-point scale explaining how much a customer liked a product, ranging from "Not very much" to "Yes, a lot"). - Assumption #2: You have
**one independent variable**that consists of**two categorical**,**independent groups**(i.e., a**dichotomous variable**). Example independent variables that meet this criterion include gender (two groups: "males" or "females"), employment status (two groups: "employed" or "unemployed"), transport type (two groups: "bus" or "car"), smoker (two groups: "yes" or "no"), trial (two groups: "intervention" or "control"), and so forth. - Assumption #3: You should have
**independence of observations**, which means that there is no relationship between the observations in each group of the independent variable or between the groups themselves. For example, there must be different participants in each group with no participant being in more than one group. This is more of a study design issue than something you can test for, but it is an important assumption of the Mann-Whitney U test. If your study fails this assumption, you will need to use another statistical test instead of the Mann-Whitney U test (e.g., a**Wilcoxon signed-rank test**). - Assumption #4: You must determine whether the
**distribution of scores for both groups of your independent variable**(e.g., the distribution of scores for "males" and the distribution of scores for "females" for the independent variable, "gender") have the**same shape**or a**different shape**. This will determine how you interpret the results of the Mann-Whitney U test. Since this is a critical assumption of the Mann-Whitney U test, and will affect how to work your way through this guide, we discuss this further in the next section.

Note: Practically speaking, your **independent variable** can actually have **three or more groups** (e.g., the independent variable, "transport type", could have four groups: "bus", "car", "train" and "plane"). However, when you run the Mann-Whitney U test procedure in SPSS, you will need to decide which two groups you want to compare (e.g., you could compare "bus" and "car", or "bus" and "plane", and so forth).

If you are unfamiliar with any of the above terms, you might want to read our Types of variable guide or use our **Statistical Test Selector** to check you are using the correct test before going any further, which can be accessed by subscribing to Laerd Statistics.