The Mann-Whitney U test, also known as the Wilcoxon rank-sum test, is a nonparametric test of the null hypothesis that two samples come from the same population against an alternative hypothesis, especially that a particular population tends to have larger values than the other.
The Mann-Whitney U test is used when your data do not meet the assumptions required for a t-test. It is a nonparametric test that allows you to determine if there are differences between two groups on a ranked dependent variable. It's often used in fields such as psychology, education, and other social and health sciences.
The Mann-Whitney U test has several assumptions. It assumes that the dependent variable is at least ordinal, which means that it is rank-ordered. It also assumes that the independent variable is categorical with two categories or groups. Lastly, it assumes independence of observations, which means that there is no relationship between the observations in each group or between the groups themselves.
The Mann-Whitney U test is used in a variety of research contexts. For example, it could be used to test whether there is a difference in test scores between male and female students, or whether a new drug has different effects than a standard drug.
Rank the data: Combine all data from the two groups into one data set and rank the data from lowest to highest. Assign ranks to each data point.
Calculate U: Calculate U for each group. U is the sum of the ranks in each group minus the smallest possible rank that each group could have.
Find the critical value of U: The critical value of U is found in a table of critical values and is based on the sample sizes of the two groups.
Decision: If the calculated U is less than or equal to the critical value of U, reject the null hypothesis.
If the U value calculated is less than the critical U value from the table, then the null hypothesis is rejected and it is concluded that there is a significant difference between the two groups. If the calculated U value is greater than the critical U value, then the null hypothesis is not rejected and it is concluded that there is not a significant difference between the two groups.
In conclusion, the Mann-Whitney U test is a powerful statistical tool that allows researchers to test hypotheses about ranked data. It is particularly useful when the assumptions of a t-test cannot be met.