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 a test of difference in medians between two populations.

2. How Does the Calculator Work?

The calculator uses the Mann-Whitney U formula:

Where:

• \( U1 \) — First U value (n₁n₂ + n₁(n₁+1)/2 - R₁)
• \( U2 \) — Second U value (n₁n₂ + n₂(n₂+1)/2 - R₂)

Explanation: The test statistic U is the smaller of U1 and U2, which are calculated from the sample sizes and rank sums of the two groups being compared.

3. Importance of U Value Calculation

Details: The U value is crucial for determining whether there is a statistically significant difference between two independent samples when the assumptions of the t-test are not met (non-normal distributions or ordinal data).

4. Using the Calculator

Tips: Enter both U1 and U2 values (calculated from your data). The calculator will determine the smaller U value which is used for hypothesis testing.

5. Frequently Asked Questions (FAQ)

Q1: When should I use the Mann-Whitney U test?
A: Use it when you have two independent samples and either ordinal data or interval/ratio data that doesn't meet normality assumptions.

Q2: How do I interpret the U value?
A: Compare your calculated U to critical values from Mann-Whitney tables or use it to calculate a p-value to determine statistical significance.

Q3: What's the difference between U and W statistics?
A: W is the rank sum statistic, while U is derived from W and adjusts for sample sizes. They're related but different test statistics.

Q4: Are there assumptions for the Mann-Whitney test?
A: Yes, it assumes independence of observations and that the two distributions have the same shape (though not necessarily the same median).

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