Mann-Whitney U Test Calculator

Perform a Mann-Whitney U test to determine if there is a significant difference between two independent samples.

Embed Mann-Whitney U Test Calculator Widget

About Mann-Whitney U Test Calculator

The Mann-Whitney U Test Calculator performs the Mann-Whitney U test, a nonparametric test used to determine whether there is a significant difference between two independent samples.

What is the Mann-Whitney U Test?

The Mann-Whitney U test (also known as the Wilcoxon rank-sum test) is a nonparametric statistical test that assesses whether two independent samples come from the same distribution. It is used when the data do not meet the assumptions necessary for a t-test, particularly the assumption of normality.

The test statistic \( U \) is calculated based on the ranks of the combined data from both samples.

How to Calculate the Mann-Whitney U Statistic

The Mann-Whitney U statistic is calculated using the following formulas:

\( U_1 = n_1 n_2 + \frac{n_1(n_1 + 1)}{2} - R_1 \)

\( U_2 = n_1 n_2 + \frac{n_2(n_2 + 1)}{2} - R_2 \)

\( U = \min(U_1, U_2) \)

Where:
\( n_1, n_2 \) = Sample sizes of Sample 1 and Sample 2
\( R_1, R_2 \) = Sum of ranks for Sample 1 and Sample 2
\( U \) = Mann-Whitney U statistic

Interpreting the Results

A small \( U \) value suggests a difference between the samples.
The p-value indicates the probability of observing the data if the null hypothesis (no difference) is true.
A p-value ≤ 0.05 typically suggests a significant difference between the samples.

Use Cases of the Mann-Whitney U Test

The Mann-Whitney U test is widely used in various fields:

Medicine: Comparing the effectiveness of treatments when data are not normally distributed.
Psychology: Assessing differences in responses between two groups.
Business: Evaluating customer satisfaction scores between two independent groups.