How to perform a Mann-Whitney U test?

To perform a Mann-Whitney U test, first rank the data from lowest to highest.

The Mann-Whitney U test is a non-parametric test used to compare two independent groups. It is used when the data does not meet the assumptions of a parametric test, such as the t-test. The first step in performing a Mann-Whitney U test is to rank the data from lowest to highest, regardless of which group it belongs to. If there are ties, assign each tied value the average of the ranks it would have received if it were not tied.

Next, calculate the U statistic. The U statistic is the smaller of two values: U1 and U2. U1 is the sum of the ranks in the first group, and U2 is the sum of the ranks in the second group. If the sample sizes are equal, U1 and U2 can be calculated using the following formula:

U1 = n1n2 + n1(n1 + 1)/2 - ΣR1
U2 = n1n2 + n2(n2 + 1)/2 - ΣR2

Where n1 and n2 are the sample sizes of the two groups, ΣR1 is the sum of the ranks in the first group, and ΣR2 is the sum of the ranks in the second group.

Finally, compare the U statistic to a critical value from a Mann-Whitney U table. The critical value depends on the sample sizes and the desired level of significance. If the calculated U statistic is less than or equal to the critical value, then there is no significant difference between the two groups. If the calculated U statistic is greater than the critical value, then there is a significant difference between the two groups.

In conclusion, the Mann-Whitney U test is a non-parametric test used to compare two independent groups. It involves ranking the data, calculating the U statistic, and comparing it to a critical value from a table.