Mann-Whitney U Test Calculator

Sample Size of First Group (n1):

Sample Size of Second Group (n2):

Sum of Ranks in First Group (R1):

Calculate

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:

1. Enter the sample size of the first group (n1).
2. Enter the sample size of the second group (n2).
3. Enter the sum of ranks in the first group (R1).
4. 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:

1. What is the Mann-Whitney U Test?
   • The Mann-Whitney U Test is a non-parametric test used to compare two independent groups.
2. 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.
3. 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.
4. Can I use the Mann-Whitney U Test for small sample sizes?
   • Yes, it is suitable for small sample sizes.
5. What if my data is not ordinal?
   • The Mann-Whitney U Test requires ordinal data.
6. Is the Mann-Whitney U Test sensitive to outliers?
   • No, it is not sensitive to outliers.
7. 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.
8. Can I perform a one-tailed test with the Mann-Whitney U Test?
   • Yes, you can perform both one-tailed and two-tailed tests.
9. What if my sample sizes are unequal?
   • The Mann-Whitney U Test can handle unequal sample sizes.
10. 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.