1. What is the Mann-Whitney U Test?

The Mann-Whitney U test is a non-parametric statistical test that compares two independent groups. It's used when the data doesn't meet the assumptions of the t-test, particularly when the data isn't 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 populations with the same distribution.

3. Importance of Mann-Whitney U Test

Details: This test is crucial for comparing two independent samples when parametric assumptions aren't met. It's robust to outliers and works with ordinal data or continuous data that isn't 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 numbers.

5. Frequently Asked Questions (FAQ)

Q1: When should I use Mann-Whitney U instead of t-test?
A: Use it when your data is ordinal or when continuous data fails normality tests, especially with small sample sizes.

Q2: How do I interpret the U value?
A: The U value represents the number of times a score from one group precedes a score from the other group. Smaller U values indicate greater difference between groups.

Q3: What's the difference between Wilcoxon and Mann-Whitney?
A: They're essentially the same test. Wilcoxon rank-sum test is equivalent to Mann-Whitney U test, just calculated slightly differently.

Q4: What are the assumptions of this test?
A: The test assumes independence of observations, ordinal or continuous data, and that the two distributions have similar shapes.

Q5: How do I determine significance?
A: Compare your U value to critical values tables or use statistical software to get a p-value. The calculator provides the U statistic which you would then compare.