1. What is the Mann-Whitney U Test?

The Mann-Whitney U test is a nonparametric test of the null hypothesis that the distribution underlying sample X is the same as the distribution underlying sample Y. It is often used as an alternative to the independent samples t-test when the data is not normally distributed.

2. How Does the Calculator Work?

The calculator uses the Mann-Whitney U formula:

Where:

• \( n_1 \) — Sample size of group 1
• \( n_2 \) — Sample size of group 2
• \( R_1 \) — Sum of ranks for group 1

Explanation: The test compares the rank sums of two independent samples to determine if they come from the same distribution.

3. Importance of U Test

Details: The Mann-Whitney U test is crucial for comparing two independent groups when the assumptions of the t-test are not met, particularly when data is ordinal or not normally distributed.

4. Using the Calculator

Tips: Enter the sample sizes for both groups and the sum of ranks for group 1. All values must be positive integers (for sample sizes) and positive numbers (for rank sums).

5. Frequently Asked Questions (FAQ)

Q1: When should I use the Mann-Whitney U test?
A: Use it when you have two independent groups and your data is ordinal or not normally distributed.

Q2: What does the U value represent?
A: The U value represents the number of times a score from one group precedes a score from the other group.

Q3: How do I interpret the U value?
A: Smaller U values indicate greater difference between groups. Compare your U value to critical values tables or use statistical software for p-value calculation.

Q4: What's the difference between Wilcoxon and Mann-Whitney tests?
A: They are essentially the same test. Wilcoxon rank-sum test is equivalent to Mann-Whitney U test.

Q5: Can I use this for paired samples?
A: No, for paired samples you should use the Wilcoxon signed-rank test instead.