R vs SAS Non-parametric Analysis - Friedman test

library(tidyverse)
library(rstatix) 
library(ggpubr)

Data used

Friedman’s test is used when you have one within-subjects independent variable with two or more levels and a dependent variable that is not interval and normally distributed (but at least ordinal). To build such unreplicated blocked data, we’ll create a data frame called df_bp from random number. In df_bp : dependent variable bp is randomly generated; Block: subjid ; Group: time_point.

set.seed(123)

df_bp = data.frame(bp = runif(n = 50, 138, 200)) %>% 
  mutate(subjid = as.factor(row_number() %% 5),  
         time_point = as.factor((row_number()-1) %/% 5 + 1))

head(df_bp)

        bp subjid time_point
1 155.8298      1          1
2 186.8749      2          1
3 163.3566      3          1
4 192.7471      4          1
5 196.3090      0          1
6 140.8245      1          2

Let’s see distribution of df_bp

ggpubr::ggboxplot(df_bp, x = "time_point", y = "bp", add = "jitter")

Example Code using {rstatix}

In R, friedman_test can be used to compare multiple means of rank in bp grouped by time_point, stratified by subjid.

res.fried <- df_bp %>% 
  friedman_test(bp ~ time_point | subjid)
res.fried

# A tibble: 1 × 6
  .y.       n statistic    df     p method       
* <chr> <int>     <dbl> <dbl> <dbl> <chr>        
1 bp        5      10.9     9 0.284 Friedman test

Example Code using {PROC FREQ}

In SAS, CMH2 option of PROC FREQ is used to perform Friedman’s test.

proc freq data=data_bp;
   tables patient*dos*bp / 
          cmh2 scores=rank noprint;
run;

Comparison

The Row Mean Scores Differ statistic of SAS result is compared with statistic of R result, together with p-value.

Analysis	Supported in R	Supported in SAS	Results Match
Friedman Test	Yes	Yes	Yes

Comparison Results from more data

Friedman’s chi-suqare approximation varies when the number of blocks or the number of groups in the randomized block design differs. Similar comparison is done when number of block subjid ranges from 4 to 20 and number of group time_point ranges from 2 to 6. All results yield exact match (Comparison criterion is set to the tenth decimal place).

Summary and Recommendation

The R friedman test is comparable to SAS. Comparison between SAS and R show identical results for the datasets tried. The rstatix package friedman_test() function is very similar to SAS in the output produced.

References

R friedman_test() documentation: https://search.r-project.org/CRAN/refmans/rstatix/html/friedman_test.html

SAS PROC FREQ documentation: https://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_freq_sect033.htm

Session Info

─ Session info ───────────────────────────────────────────────────────────────
 setting  value
 version  R version 4.4.3 (2025-02-28)
 os       Ubuntu 24.04.2 LTS
 system   x86_64, linux-gnu
 ui       X11
 language (EN)
 collate  C.UTF-8
 ctype    C.UTF-8
 tz       Europe/London
 date     2025-03-13
 pandoc   NA (via rmarkdown)

─ Packages ───────────────────────────────────────────────────────────────────
 ! package * version date (UTC) lib source
 P rstatix * 0.7.2   2023-02-01 [?] RSPM (R 4.4.0)

 [1] /home/michael/source/CAMIS/renv/library/linux-ubuntu-noble/R-4.4/x86_64-pc-linux-gnu
 [2] /opt/R/4.4.3/lib/R/library

 P ── Loaded and on-disk path mismatch.

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