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)
The number of cases of each pair (n)

The comparison table (one row per pair) is stored as $results (also available as $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
Z is computed from the differences var2 - var1, like wilcoxon_test(x = var1, y = var2) and the SPSS pair "var2 - var1"
As in SPSS, Z comes from the smaller rank sum and is never positive; z_based_on names that sum (SPSS's footnote)
Based on negative ranks: values in var2 (Var 2) tend to be higher
Based on positive ranks: values in var1 (Var 1) tend to be higher

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:

Computes differences between the two measurements
Ranks the absolute differences
Computes a Z-statistic based on the rank sums
Uses normal approximation with tie correction

Which Cases Are Used

Each pair uses all cases with valid values on both of its variables (pairwise deletion), exactly like the individual SPSS NPAR TESTS /WILCOXON tests these results are validated against. friedman_test() uses only cases complete on all variables (listwise, as SPSS /FRIEDMAN), so a pair's n can be larger than the Friedman N.

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 analyses

When the friedman_test() result is weighted, each pairwise test uses the same frequency-weighted signed-rank formulas. With all weights equal to 1 they reproduce the unweighted tests exactly. Weighted results are not compared with SPSS output; see vignette("spss-compatibility").

Each pairwise comparison uses wilcoxon_test() logic internally

References

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

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.