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Find Which Specific Measurements Differ After Friedman Test

Source: R/pairwise_wilcoxon.R
pairwise_wilcoxon.Rd

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

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) Results
#> ----------------------------------------------------
#> 
#> - Variables: trust_government, trust_media, trust_science
#> - P-value adjustment: Bonferroni
#> - Number of comparisons: 3
#> 
#> ------------------------------------------------------------ 
#>             Var 1         Var 2      Z p (unadj) p (adj) Sig 
#>  trust_government   trust_media -5.097     <.001   <.001 *** 
#>  trust_government trust_science 25.945     <.001   <.001 *** 
#>       trust_media trust_science 29.091     <.001   <.001 *** 
#> ------------------------------------------------------------ 
#> 
#> 
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#> 
#> Interpretation:
#> - Positive Z: First variable tends to have higher values
#> - Negative Z: Second variable tends to have higher values
#> - p-values are adjusted for multiple comparisons

# With Holm correction (less conservative)
friedman_result %>% pairwise_wilcoxon(p_adjust = "holm")
#> Pairwise Wilcoxon Post-Hoc Test (Holm) Results
#> ----------------------------------------------
#> 
#> - Variables: trust_government, trust_media, trust_science
#> - P-value adjustment: Holm
#> - Number of comparisons: 3
#> 
#> ------------------------------------------------------------ 
#>             Var 1         Var 2      Z p (unadj) p (adj) Sig 
#>  trust_government   trust_media -5.097     <.001   <.001 *** 
#>  trust_government trust_science 25.945     <.001   <.001 *** 
#>       trust_media trust_science 29.091     <.001   <.001 *** 
#> ------------------------------------------------------------ 
#> 
#> 
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#> 
#> Interpretation:
#> - Positive Z: First variable tends to have higher values
#> - Negative Z: Second variable tends to have higher values
#> - p-values are adjusted for multiple comparisons

# With Benjamini-Hochberg (controls false discovery rate)
friedman_result %>% pairwise_wilcoxon(p_adjust = "BH")
#> Pairwise Wilcoxon Post-Hoc Test (Benjamini-Hochberg) Results
#> ------------------------------------------------------------
#> 
#> - Variables: trust_government, trust_media, trust_science
#> - P-value adjustment: Benjamini-Hochberg
#> - Number of comparisons: 3
#> 
#> ------------------------------------------------------------ 
#>             Var 1         Var 2      Z p (unadj) p (adj) Sig 
#>  trust_government   trust_media -5.097     <.001   <.001 *** 
#>  trust_government trust_science 25.945     <.001   <.001 *** 
#>       trust_media trust_science 29.091     <.001   <.001 *** 
#> ------------------------------------------------------------ 
#> 
#> 
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#> 
#> Interpretation:
#> - Positive Z: First variable tends to have higher values
#> - Negative Z: Second variable tends to have higher values
#> - p-values are adjusted for multiple comparisons

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

fw_weighted %>% pairwise_wilcoxon()
#> Weighted Pairwise Wilcoxon Post-Hoc Test (Bonferroni) Results
#> -------------------------------------------------------------
#> 
#> - Variables: trust_government, trust_media, trust_science
#> - Weights variable: sampling_weight
#> - P-value adjustment: Bonferroni
#> - Number of comparisons: 3
#> 
#> ------------------------------------------------------------ 
#>             Var 1         Var 2      Z p (unadj) p (adj) Sig 
#>  trust_government   trust_media -5.033     <.001   <.001 *** 
#>  trust_government trust_science 25.997     <.001   <.001 *** 
#>       trust_media trust_science 29.095     <.001   <.001 *** 
#> ------------------------------------------------------------ 
#> 
#> 
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#> 
#> Interpretation:
#> - Positive Z: First variable tends to have higher values
#> - Negative Z: Second variable tends to have higher values
#> - p-values are adjusted for multiple comparisons

# 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) Results
#> ----------------------------------------------------
#> 
#> - Variables: trust_government, trust_media, trust_science
#> - P-value adjustment: Bonferroni
#> - Number of comparisons: 3
#> 
#> 
#> Group: region = East
#> --------------------
#> ------------------------------------------------------------ 
#>             Var 1         Var 2      Z p (unadj) p (adj) Sig 
#>  trust_government   trust_media -2.727     0.006   0.019   * 
#>  trust_government trust_science 11.635     <.001   <.001 *** 
#>       trust_media trust_science 13.820     <.001   <.001 *** 
#> ------------------------------------------------------------ 
#> 
#> 
#> Group: region = West
#> --------------------
#> ------------------------------------------------------------ 
#>             Var 1         Var 2      Z p (unadj) p (adj) Sig 
#>  trust_government   trust_media -4.346     <.001   <.001 *** 
#>  trust_government trust_science 23.191     <.001   <.001 *** 
#>       trust_media trust_science 25.630     <.001   <.001 *** 
#> ------------------------------------------------------------ 
#> 
#> 
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#> 
#> Interpretation:
#> - Positive Z: First variable tends to have higher values
#> - Negative Z: Second variable tends to have higher values
#> - p-values are adjusted for multiple comparisons