Mann-Whitney U test

Mann-Whitney U test

Mann-Whitney U test is a non-parametric statistical technique. It is used to analyze differences between the medians of two data sets. It can be used in place of a t-test for independent samples in cases where the values within the sample do not follow the normal or t-distribution but also when the distribution of values is unknown. In measurable on an ordinary scale and comparable in size. The fact that all values are compared makes it distinct from the t-test, which compares the sample means. The Mann-Whitney U is also used to test the null hypothesis, subject to both samples coming from the same basic set or having the same median value. 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 variablethat 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. 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).

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.

 Assumptions of the Mann-Whitney test: random samples from populations independence within samples and mutual independence between samples measurement scale is at least ordinal A confidence interval for the difference between two measures of location is provided with the sample medians. The assumptions of this method are slightly different from the assumptions of the Mann-Whitney test: random samples from populations independence within samples and mutual independence between samples two population distribution functions are identical apart from a possible difference in location parameters