The Mann-Whitney U calculator is a tool designed to perform the Mann-Whitney U test, which compares the medians of two independent groups. It helps determine if there are differences in the central tendency of two datasets without making assumptions about the underlying distributions of those datasets. This makes it particularly valuable in research fields where data may not meet the normality criterion required for t-tests.
Formula of Mann-Whitney U Calculator
The calculation of the Mann-Whitney U statistic involves several steps centered around the ranks of data points within the combined dataset of two groups:
Ranking the Data
- Assign a Rank: Each data point in the combined dataset of two groups is ranked. Ties are given a rank equal to the average of the ranks they would have otherwise occupied.
Summing the Ranks for Each Group
- Calculate Rank Sums: Separate sums of ranks (T1T1 for group 1 and T2T2 for group 2) are calculated.
Calculating U
The U statistic is the key output of the Mann-Whitney U test and is calculate as follows:
- n1 and n2 are the sample sizes of the two groups.
- T1 is the sum of the ranks in the first group.
This formula determines which of the sums of ranks is smaller, which in turn helps identify if one group tends to have higher values than the other.
Table of General Terms and Useful Conversions
| Term | Definition |
|---|---|
| Rank | The position of a data point in the ordered list of all data points |
| Tie | Occurs when two or more data points have the same value |
| Sample Size (n) | The number of observations in the sample |
| Sum of Ranks (T) | The total of the ranks for the sample |
| U-Value | The test statistic calculated to determine differences |
| n₁ (Size of Group 1) | n₂ (Size of Group 2) | Minimum U Value for Significance (α=0.05) |
|---|---|---|
| 5 | 8 | 13 |
| 10 | 10 | 23 |
| 15 | 15 | 34 |
| 20 | 20 | 45 |
| 25 | 25 | 57 |
Example of Mann-Whitney U Calculator
Consider two groups of data, Group 1 with sizes 5, and Group 2 with sizes 13. After ranking all data and calculating sums of ranks, suppose T1T1 is 34. The U value would be calculate as follows:
U = 5 * 13 + (5*(5+1)/2) - 34 = 40
This result can help assess whether the two groups differ significantly in their central tendencies.
Most Common FAQs
The Mann-Whitney U test is use to assess whether two independent samples come from the same distribution. It is an alternative to the t-test when data does not meet normality requirements.
Unlike the t-test, the Mann-Whitney U test does not assume a normal distribution of the data and is use on ordinal data to test for differences in median between two independent samples.
A significant result in the Mann-Whitney U test suggests a difference in the central tendencies of the groups involved, implying that one group typically ranks higher than the other.
