Kruskal-Wallis Test Calculator

Results:

Understanding Kruskal-Wallis Test

Test Statistics

H = [(12 / N(N+1)) × ∑(R²ᵢ/nᵢ)] - 3(N+1)

Where:

  • N = Total number of observations
  • Rᵢ = Sum of ranks for group i
  • nᵢ = Size of group i

Test Assumptions

Independent samples and ordinal data

Distribution

Approximates chi-square with k-1 df

Critical Values

Based on chi-square distribution

Interpretation

Null Hypothesis

All groups have same distribution

Alternative Hypothesis

At least one group differs

Decision Rule

Reject H₀ if H > critical value

Applications

Medical Research

Treatment effectiveness comparison

Social Sciences

Behavioral studies analysis

Quality Control

Process performance evaluation

Advanced Properties and Applications

Statistical Properties

  • Asymptotic Efficiency
  • Ties Adjustment
  • Power Analysis
  • Effect Size Measures

Advanced Applications

  • Multiple Comparisons
  • Post-hoc Analysis
  • Sample Size Planning
  • Robustness Studies

Real-world Examples

  • Clinical Trials
  • Educational Research
  • Market Analysis
  • Environmental Studies