The wilcoxon rank sum test calculator is used to compare two independent groups of samples. This test, also known as the Mann-Whitney U test, helps determine if there’s a significant difference between the two groups by ranking the combined data and analyzing the sum of ranks for each group.
Wilcoxon Rank-Sum Test Calculation Chart
| Group A | Group B | Combined Ranks | Rank A | Rank B |
|---|---|---|---|---|
| 15 | 12 | 12 | – | 1 |
| 18 | 14 | 14 | – | 2 |
| 22 | 16 | 15 | 3 | – |
| 24 | 19 | 16 | – | 4 |
| 27 | 23 | 18 | 5 | – |
| 25 | 19 | – | 6 | |
| 22 | 7 | – | ||
| 23 | – | 8 | ||
| 24 | 9 | – | ||
| 25 | – | 10 | ||
| 27 | 11 | – |
Wilcoxon Rank-Sum Test Formula
The Wilcoxon Rank-Sum Test formula is:
W = R₁ - [n₁(n₁ + 1)] / 2Where:
- W is the test statistic
- R₁ is the sum of ranks for Group A
- n₁ is the sample size of Group A
Using the data from our table:
- R₁ = 3 + 5 + 7 + 9 + 11 = 35
- n₁ = 5
Calculating W:
W = 35 - [5(5 + 1)] / 2
W = 35 - 15 = 20This W value is then compared to critical values or used to calculate a p-value to determine statistical significance.
What is Wilcoxon Rank-Sum Test?
The Wilcoxon Rank-Sum Test is a non-parametric statistical test used to compare two independent groups of samples.
It’s particularly useful when the data doesn’t follow a normal distribution or when dealing with ordinal data.
The test works by combining and ranking all the data from both groups, then comparing the sum of ranks for each group to determine if there’s a significant difference between them.