Mann-Whitney U test is the alternative test to the t-test. Mann-Whitney U test is a non-parametric test that is used to compare two population means that come from the same population. Mann-Whitney U test is also used to test whether two population means are equal or not. Mann-Whitney U test was developed by Wilcoxon in 1945. It is used for equal sample sizes, and is used to test the median of two populations. Usually Mann-Whitney U test is used when the data is ordinal. Wilcoxon rank sum, Kendall’s and Mann-Whitney U test are similar tests and in the case of ties, Mann-Whitney U test is equivalent to the chi-square test.
Assumptions in Mann-Whitney U test:
Mann-Whitney U test is a non parametric test, hence it does not assume any assumptions related to the distribution. There are, however, some assumptions that are assumed in Mann-Whitney U test. The following are the assumptions for Mann-Whitney U Test:
1. Mann-Whitney U test assumes that the sample drawn from the population is random.
2. In Mann-Whitney U test, Independence within the samples and mutual independence is assumed.
3. Ordinal measurement scale is assumed in Mann-Whitney U test.
Calculation of Mann-Whitney U test:
To calculate the value of Mann-Whitney U test, we use the following formula:
Where:
U=Mann-Whitney U test
N1 = sample size one
N2= Sample size two
Ri = Rank of the sample size
Mann-Whitney U test in SPSS:
Most of the statistical software has the option for Mann-Whitney U test. In SPSS, as we click on the “analysis menu,” there is an option of a “nonparametric test.” In Non-parametric test, we will select two independent sample tests. As the window appears, we will select the dependent variable and insert them into the test variable’s list. After inserting the dependent variables, we will select the independent variables and insert them as the grouping variables and define the group by clicking on the “grouping” option. We can select the “Mann-Whitney U test” from the test statistics given in a window and select “descriptive statistics” from the option menu. Finally, click on the “ok” button. After clicking the ok button, the following results window will appear in front of us:
In SPSS, the first table will show the rank tables which contain the descriptive statistics and the mean and sum of ranks. Table 1 shows descriptive statistics for Mann-Whitney U tests.
Table 1
In Mann-Whitney U test, the second table shows the result of the computed Mann-Whitney U test statistics and it is associated with its significance value. In Mann-Whitney U test, P value for two tailed helps us to decide whether or not the mean (median) of two populations are equal. For example, in table significance level at 10%, only research question V5 shows the significant mean difference for two groups for the Mann-Whitney U test. Other research questions show non significant differences between the two groups at 5% and 10% significance level.
Table 2
Use of Mann-Whitney U test:
Mann-Whitney U test is used for every field, but in Psychology, Medical/Nursing and Business it is used frequently. For example, in Psychology, Mann-Whitney U test is used to compare attitude or behavior, etc. In medicine, Mann-Whitney U test is used to know the effect of two medicines and whether they are equal or not. It is also used to know whether or not a particular medicine cures the ailment or not. In Business, Mann-Whitney U test can be used to know the preferences of different people and it can be used to see if that changes depending on location.
