Enter the sample sizes of the first and second groups, and the sum of the ranks in the first group into the calculator to determine the U statistic.
Mann-Whitney U Test Formula
The following formula is used to calculate the U statistic in a Mann-Whitney U Test.
U = n1*n2 + (n1*(n1+1))/2 - R1
Variables:
- U is the Mann-Whitney U statistic
- n1 is the sample size of the first group
- n2 is the sample size of the second group
- R1 is the sum of the ranks in the first group
To calculate the U statistic, multiply the sample size of the first group by the sample size of the second group. Add the result to half of the product of the sample size of the first group and the sum of the sample size of the first group and 1. Subtract the sum of the ranks in the first group from the result.
What is a Mann-Whitney U Test?
A Mann-Whitney U test, also known as Wilcoxon rank-sum test, is a nonparametric statistical test that is used to determine if there are differences between two independent groups in terms of their ranks on a particular variable. It is often used when the data does not meet the assumptions of a standard t-test, such as normal distribution. The test essentially ranks all the data from both groups together, then compares the sum of ranks for each group to see if they significantly differ from what would be expected if the groups were identical.
How to Calculate Mann-Whitney U Test?
The following steps outline how to calculate the Mann-Whitney U statistic.
- First, determine the sample size of the first group (n1).
- Next, determine the sample size of the second group (n2).
- Next, calculate the sum of the ranks in the first group (R1).
- Next, use the formula U = n1 * n2 + (n1 * (n1 + 1)) / 2 – R1 to calculate the Mann-Whitney U statistic.
- Finally, calculate the U value using the given variables.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge.
n1: Sample size of the first group = 10
n2: Sample size of the second group = 8
R1: Sum of the ranks in the first group = 78
