Wilcoxon Rank-Sum Test Calculator
Non-parametric test using rank sums to compare two independent samples
Test Configuration
Detected 0 valid values
Detected 0 valid values
Example: Sleep Quality Study
Control Group (A)
Data: 5.2, 6.1, 4.8, 5.9, 5.5, 6.0, 5.7
Sample size: n₁ = 7
Sleep hours: Standard treatment
New Treatment (B)
Data: 7.2, 8.1, 7.8, 8.5, 7.9, 8.0
Sample size: n₂ = 6
Sleep hours: New sleep aid
Expected Result
New treatment shows higher sleep quality
Conclusion: Significant evidence of treatment effectiveness
When to Use Wilcoxon Rank-Sum Test
Two Independent Samples
Comparing two groups with different subjects
Non-Normal Data
Data doesn't follow normal distribution
Small Sample Sizes
Works well with small samples (n < 30)
Rank-Based Analysis
Uses sum of ranks as test statistic
Wilcoxon vs Mann-Whitney
Same Test: Both tests are mathematically equivalent and always give the same conclusion
Different Statistics: Wilcoxon uses rank sums (W), Mann-Whitney uses U statistic
Relationship: U₁ = W - n₁(n₁+1)/2
Choice: Use whichever statistic you prefer or is required by your context
Understanding the Wilcoxon Rank-Sum Test
What is the Wilcoxon Rank-Sum Test?
The Wilcoxon rank-sum test is a non-parametric statistical test used to determine whether two independent samples come from populations with the same distribution. It uses the sum of ranks from one sample as the test statistic, making it robust to outliers and non-normal data.
Key Advantages
- •Distribution-free: No assumption of normality required
- •Robust: Less sensitive to outliers than parametric tests
- •Small samples: Works well with small sample sizes
Key Formulas
W Statistic (Rank Sum)
W = Σ ranks in sample A
Sum of all ranks assigned to sample A
Normal Approximation
z = (W - μw) / σw
μw = n₁(n₁+n₂+1)/2, σw² = n₁n₂(n₁+n₂+1)/12
Ties Correction
σw² = σw²(1 - Ct)
Ct adjusts for tied ranks
Step-by-Step Process
- 1.Combine and rank all observations from both samples
- 2.Handle ties by assigning average ranks
- 3.Calculate sum of ranks for sample A (W statistic)
- 4.Compare with critical values or use normal approximation
Interpretation Guidelines
- •p-value < α: Reject null hypothesis (significant difference)
- •p-value ≥ α: Fail to reject null hypothesis
- •Large W: Sample A tends to have higher values
- •Small W: Sample A tends to have lower values