Permutation-Based ANOVA with Post-Hoc Pairwise Comparisons

Source: R/permutation_anova.R

Performs a permutation test for a one-way ANOVA, followed by post-hoc pairwise comparisons between group means. The function computes empirical p-values from a shared permutation distribution and adjusts for multiple testing.

permutation_anova(
  response,
  group,
  B = 10000,
  seed = NULL,
  plot = TRUE,
  fast_pairwise = FALSE
)

Arguments

response

A numeric vector of response values.

group

A factor vector indicating group membership for each observation.

B

Number of permutations to perform. Default is 10,000.

seed

Optional integer to set random seed for reproducibility.

plot

Logical; if TRUE, plots the permutation distributions for the F-statistic and pairwise differences. Default is TRUE.

fast_pairwise

Logical; if TRUE, will randomly sample only one pair mean difference for each permutation. If FALSE (default), will calculate every pairwise difference for each permutation.

Value

A list containing:

observed_F

Observed F-statistic from the linear model.

permutation_p

Permutation-based p-value for the global test.

perm_F_distribution

Vector of F-statistics from permuted datasets.

pairwise_results

Data frame with observed pairwise differences and p-values (raw and adjusted using Bonferroni, Holm, and BH).

perm_pairwise_distribution

Vector of all permuted pairwise mean differences pooled across all comparisons.

Examples

set.seed(123)
group <- factor(rep(c("A", "B", "C"), each = 10))
response <- rnorm(30) + rep(c(0, 0.5, 1), each = 10)
result <- permutation_anova(response, group, B = 1000, seed = 123)

result$pairwise_results
#>       comparison  obs_diffs      pval p_bonf    p_holm     p_FDR
#> A - B      A - B -0.6339963 0.1426667  0.428 0.4280000 0.3730000
#> A - C      A - C -0.5008155 0.2486667  0.746 0.4973333 0.3730000
#> B - C      B - C  0.1331808 0.7646667  1.000 0.7646667 0.7646667