R - pairwise_t_test Test Statistics Unchanged When Switching Between Pooled Standard Deviation and non-Pooled Stardard Deviation

Question

While reviewing pairwise t-tests as a post hoc for one way repeated measures ANOVA I noticed an oddity. The test statistic for pair_t_test in the rstatix library does not change when I pool the standard deviation -- in fact none of the output changes.

My understanding is that the whole point of pooling the standard deviation is to more accurately estimate the test statistic. However, while trying this out I can't find a difference in the output (see below).

Is my understanding incorrect? What effect should a pooled standard deviation have on multiple pairwise comparisons (sphericity notwithstanding)?

I used the following data setup:

library(rstatix)
library(tidyverse)

selfesteem.test <- selfesteem %>%
  gather(key = "time", value = "score", t1, t2, t3) %>%
  convert_as_factor(id, time)

With pooled standard deviation in the following code:

selfesteem.test %>%
  pairwise_t_test(
    score ~ time,
    paired = TRUE,
    p.adjust.method = "bonferroni",
    pool.sd = TRUE
  )

Resulting in:

# A tibble: 3 x 10
  .y.   group1 group2    n1    n2 statistic    df           p    p.adj p.adj.signif
* <chr> <chr>  <chr>  <int> <int>     <dbl> <dbl>       <dbl>    <dbl> <chr>       
1 score t1     t2        10    10     -4.97     9 0.000772    0.002    **          
2 score t1     t3        10    10    -13.2      9 0.000000334 0.000001 ****        
3 score t2     t3        10    10     -4.87     9 0.000886    0.003    **          

The following code:

selfesteem.test %>%
  pairwise_t_test(
    score ~ time,
    paired = TRUE,
    p.adjust.method = "bonferroni",
    pool.sd = FALSE
  )

Results in the same:

# A tibble: 3 x 10
  .y.   group1 group2    n1    n2 statistic    df           p    p.adj p.adj.signif
* <chr> <chr>  <chr>  <int> <int>     <dbl> <dbl>       <dbl>    <dbl> <chr>       
1 score t1     t2        10    10     -4.97     9 0.000772    0.002    **          
2 score t1     t3        10    10    -13.2      9 0.000000334 0.000001 ****        
3 score t2     t3        10    10     -4.87     9 0.000886    0.003    ** 

Answer 1

According to ?pairwise_t_test

Pooling does not generalize to paired tests so pool.sd and paired cannot both be TRUE.

If pool.sd = FALSE the standard two sample t-test is applied to all possible pairs of groups. This method calls the t.test(), so extra arguments, such as var.equal are accepted.

Also, the Usage does show the negation (!)

pairwise_t_test( data, formula, comparisons = NULL, ref.group = NULL, p.adjust.method = "holm", paired = FALSE, pool.sd = !paired, detailed = FALSE, ... )