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 1 is the same as the distribution underlying sample 2. It's used when you can't assume your data comes from a normal distribution (non-normal data).

2. How Does the Calculator Work?

The calculator uses the Mann-Whitney U formula:

Where:

• \( n_1 \) — Size of first sample
• \( n_2 \) — Size of second sample
• \( R_1 \) — Sum of ranks for first sample

Explanation: The U statistic represents the number of times observations in one sample precede observations in the other sample in the ranking.

3. Importance of U Statistic

Details: The U test is particularly useful when comparing two independent samples that may not be normally distributed. It's a robust alternative to the independent samples t-test.

4. Using the Calculator

Tips: Enter the sample sizes (n1 and n2) and the sum of ranks for the first sample (R1). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

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

Q2: What does the U value represent?
A: The U value indicates the degree of separation between the two samples. A smaller U value indicates greater separation.

Q3: How do I interpret the U statistic?
A: Compare your calculated U to critical values from Mann-Whitney tables or use it to calculate a p-value for hypothesis testing.

Q4: What are the assumptions of this test?
A: The test assumes that observations are independent and that the two distributions are similar in shape (though they can differ in location).

Q5: Can I use this for small sample sizes?
A: Yes, the Mann-Whitney U test works well for small samples (typically n < 20 for each group).