KruskalWallis

Kruskal-Wallis test with post-hoc tests for multiple comparisons.

• Kruskal-Wallis Test - A non-parametric test to determine if there are statistically significant differences between groups
• Dunn's Post-Hoc Test - Pairwise comparisons to identify which specific groups differ. Uses z-statistic (normal distribution) - more conservative, fewer assumptions
• Holm Correction - Adjusts p-values to control for multiple comparisons
• Conover Test - Pairwise comparisons to identify which specific groups differ. Uses t-statistic (t-distribution) - more powerful when distributions have similar shapes, similar to Tukey's HSD for ANOVA. It is generally preferred when you have similar distribution shapes across groups, while Dunn's test is more robust when distributions differ in shape

Installation

def deps do
  [
    {:kruskal_wallis, "~> 0.2.0"}
  ]
end

Usage

groups = %{
  "A" => [1.2, 2.3, 1.8, 2.1, 1.9],
  "B" => [3.4, 4.1, 3.8, 4.5, 3.9],
  "C" => [2.1, 2.8, 2.4, 2.6, 2.3]
}

kw_result = KruskalWallis.test(groups)

# Use Dunn test (more conservative)
dunn_results = KruskalWallis.Dunn.test(kw_result, groups)

# Or use Conover test (more powerful)
conover_results = KruskalWallis.Conover.test(kw_result, groups)

Citations

References for the statistical methods implemented here; Kruskal-Wallis test, Dunn's post-hoc, Conover-Iman post-hoc, and Holm correction.

• Kruskal, W. H., & Wallis, W. A. (1952). "Use of ranks in one-criterion variance analysis." Journal of the American Statistical Association, 47(260), 583–621.
• Dunn, O. J. (1964). "Multiple comparisons using rank sums." Technometrics, 6(3), 241–252.
• Conover, W. J., & Iman, R. L. (1979). "On multiple-comparisons procedures." Los Alamos Scientific Laboratory report LA-7677-MS.
• Holm, S. (1979). "A simple sequentially rejective multiple test procedure." Scandinavian Journal of Statistics, 6(2), 65–70.