The Mann-Whitney U test, also known as the Mann-Whitney-Wilcoxon test, is a nonparametric statistical test used to determine if there is a significant difference between two independent groups. It is named after Frank Wilcoxon and Henry Mann, the statisticians who developed the test.
This test is appropriate when the data is not normally distributed or when the assumptions required by parametric tests, such as the t-test, are not met. The Mann-Whitney U test is commonly employed to compare two groups of data when the samples are small or when the data is ordinal or ranked.
The test essentially involves assigning ranks to the values in the combined dataset, combining the two groups, and then calculating the sum of ranks for each group separately. The test statistic U is then calculated based on the difference between the sums of ranks. The U value is compared to critical values from the Mann-Whitney U table or calculated using statistical software.
If the calculated U value is less than or equal to the critical value, it indicates that the two groups are significantly different. Conversely, if the calculated U value is greater than the critical value, it suggests that there is no significant difference between the two groups.
The Mann-Whitney U test is a powerful tool in statistical analysis, especially when dealing with nonparametric data or small sample sizes. It allows researchers to compare two independent groups and determine if there is a significant difference between them, without relying on strict assumptions about the data distribution.
