The Mann-Whitney U Test is a non-parametric statistical test used to compare the distributions of two independent groups. It is used when the assumptions of parametric tests like the t-test are not met.

**Formula**: The Mann-Whitney U Test formula calculates the U statistic as follows:

U = n1 * n2 + (n1 * (n1 + 1)) / 2 – R1

Where:

- n1 is the sample size of the first group.
- n2 is the sample size of the second group.
- R1 is the sum of ranks in the first group.

**How to Use**:

- Enter the sample size of the first group (n1).
- Enter the sample size of the second group (n2).
- Enter the sum of ranks in the first group (R1).
- Click the “Calculate” button to find the Mann-Whitney U Statistic (U).

**Example**: Let’s say we have two groups:

- Group 1 with a sample size of 10 (n1 = 10) and a sum of ranks of 78 (R1 = 78).
- Group 2 with a sample size of 15 (n2 = 15).

Using the formula: U = (10 * 15) + ((10 * 11) / 2) – 78 U ≈ 95

**FAQs**:

- What is the Mann-Whitney U Test?
- The Mann-Whitney U Test is a non-parametric test used to compare two independent groups.

- When should I use the Mann-Whitney U Test?
- You should use it when the assumptions of parametric tests like the t-test are not met.

- What does the U statistic represent?
- The U statistic represents the probability that a randomly selected observation from one group will be greater than a randomly selected observation from the other group.

- Can I use the Mann-Whitney U Test for small sample sizes?
- Yes, it is suitable for small sample sizes.

- What if my data is not ordinal?
- The Mann-Whitney U Test requires ordinal data.

- Is the Mann-Whitney U Test sensitive to outliers?
- No, it is not sensitive to outliers.

- How do I interpret the U statistic?
- A higher U value indicates that observations in the first group tend to be larger than those in the second group.

- Can I perform a one-tailed test with the Mann-Whitney U Test?
- Yes, you can perform both one-tailed and two-tailed tests.

- What if my sample sizes are unequal?
- The Mann-Whitney U Test can handle unequal sample sizes.

- How do I report the results of the Mann-Whitney U Test?
- Report the U statistic, significance level, and any assumptions made.

**Conclusion**: The Mann-Whitney U Test is a valuable tool for comparing two independent groups when the assumptions of parametric tests are not met. This calculator simplifies the calculation of the U statistic, making the analysis process more efficient and accessible.