Find Which Specific Measurements Differ After Friedman Test

pairwise_wilcoxon() tells you exactly which pairs of measurements differ from each other after the Friedman test finds overall differences. It performs all pairwise Wilcoxon signed-rank tests with p-value correction.

Think of it as:

• Friedman says "there are differences somewhere among the measurements"

• Pairwise Wilcoxon says "specifically, Measurement A differs from Measurement C"

• A way to make all possible pairwise comparisons for repeated measures

Usage

pairwise_wilcoxon(x, ...)

# Default S3 method
pairwise_wilcoxon(x, ...)

Arguments

x

Friedman test results from friedman_test()

...

Additional arguments passed to methods. The method for friedman_test objects accepts p_adjust (character): method for adjusting p-values for multiple comparisons. Options: "bonferroni" (default, most conservative), "holm", "BH", "hochberg", "hommel", "BY", "fdr", "none".

Value

Pairwise comparison results showing:

• Which measurement pairs are significantly different

• Z-statistics from Wilcoxon signed-rank tests

• Adjusted p-values (controlling for multiple comparisons)

Details

Understanding the Results

Z-Statistics: Based on the Wilcoxon signed-rank test for each pair

• Large absolute Z values indicate big differences between two measurements

• Positive Z: Values in var1 tend to be higher than var2

• Negative Z: Values in var2 tend to be higher than var1

Adjusted P-values: Control for multiple comparisons

• p < 0.05: Measurements are significantly different

• p >= 0.05: No significant difference between these measurements

The Wilcoxon Signed-Rank Test

For each pair of measurements, the Wilcoxon signed-rank test:

1. Computes differences between the two measurements

2. Ranks the absolute differences

3. Computes a Z-statistic based on the rank sums

4. Uses normal approximation with tie correction

P-Value Adjustment Methods

• Bonferroni (default): Most conservative, multiplies p by number of comparisons

• Holm: Step-down method, less conservative than Bonferroni

• BH: Controls false discovery rate, good for many comparisons

When to Use This

Use pairwise Wilcoxon when:

• Your Friedman test shows significant differences (p < 0.05)

• You want to know which specific measurements differ

• Your data are ordinal or violate normality assumptions

• You have repeated measures or matched groups

Relationship to Other Tests

• Non-parametric post-hoc for repeated measures (like Dunn is for independent groups)

• Follow-up to friedman_test(), like dunn_test() follows kruskal_wallis()

Weighted variants

When the parent friedman_test() result is weighted, each pairwise test uses the same frequency-weighted signed-rank formulas. SPSS NPAR TESTS ignores WEIGHT BY, so weighted results have no SPSS reference (R-only, guarded by an internal invariance suite); see vignette("spss-compatibility") for validation status.

• Each pairwise comparison uses wilcoxon_test() logic internally

References

Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80-83.

See also

friedman_test for performing Friedman tests.

wilcoxon_test for individual paired Wilcoxon tests.

dunn_test for post-hoc comparisons after Kruskal-Wallis.

Other posthoc: dunn_test(), levene_test(), scheffe_test(), tukey_test()

Examples

# Load required packages and data
library(dplyr)
data(survey_data)

# Perform Friedman followed by pairwise Wilcoxon post-hoc
friedman_result <- survey_data %>%
  friedman_test(trust_government, trust_media, trust_science)

# Pairwise Wilcoxon comparisons (default: Bonferroni)
friedman_result %>% pairwise_wilcoxon()
#> Pairwise Wilcoxon Post-Hoc Test (Bonferroni)
#>   3 comparisons, 3 significant (p < .05)
#> Use summary() for the full comparison table.

# With Holm correction (less conservative)
friedman_result %>% pairwise_wilcoxon(p_adjust = "holm")
#> Pairwise Wilcoxon Post-Hoc Test (Holm)
#>   3 comparisons, 3 significant (p < .05)
#> Use summary() for the full comparison table.

# With Benjamini-Hochberg (controls false discovery rate)
friedman_result %>% pairwise_wilcoxon(p_adjust = "BH")
#> Pairwise Wilcoxon Post-Hoc Test (Benjamini-Hochberg)
#>   3 comparisons, 3 significant (p < .05)
#> Use summary() for the full comparison table.

# With weights
fw_weighted <- survey_data %>%
  friedman_test(trust_government, trust_media, trust_science,
                weights = sampling_weight)

fw_weighted %>% pairwise_wilcoxon()
#> Pairwise Wilcoxon Post-Hoc Test (Bonferroni) [Weighted]
#>   3 comparisons, 3 significant (p < .05)
#> Use summary() for the full comparison table.

# Grouped analysis
fw_grouped <- survey_data %>%
  group_by(region) %>%
  friedman_test(trust_government, trust_media, trust_science)

fw_grouped %>% pairwise_wilcoxon()
#> Pairwise Wilcoxon Post-Hoc Test (Bonferroni)
#> [region = East]
#>   3 comparisons, 3 significant (p < .05)
#> [region = West]
#>   3 comparisons, 3 significant (p < .05)
#> Use summary() for the full comparison table.