A note from the future: as guided by the knowledgeable zmughal, I stopped trying to use MATLAB/Octave, and switched to using R, which is certainly the go-to solution for free statistics software. This is the R equivalent of the test in the given PDL::Stats test file:

library(data.table)
library(rstatix)
tdata <- data.frame(
 stringsAsFactors = FALSE,
 dv = c(3.0,2.0,1.0,5.0,2.0,1.0,5.0,3.0,1.0,4.0,1.0,2.0,3.0,5.0,5.0,3.
+0,4.0,2.0,1.0,5.0,4.0,3.0,2.0,2.0),
 id = c(0L,1L,2L,3L,0L,1L,2L,3L,0L,1L,2L,3L,0L,1L,2L,3L,0L,1L,2L,3L,0L
+,1L,2L,3L),
 w = c(0L,0L,0L,0L,0L,0L,0L,0L,1L,1L,1L,1L,1L,1L,1L,1L,2L,2L,2L,2L,2L,
+2L,2L,2L),
 b = c(0L,0L,0L,0L,1L,1L,1L,1L,0L,0L,0L,0L,1L,1L,1L,1L,0L,0L,0L,0L,1L,
+1L,1L,1L)
)
as.data.table(tdata)
tdata <- tdata %>% convert_as_factor(id, w, b)
as.data.table(tdata)
res.aov <- anova_test(
  data = tdata, dv = dv, wid = id,
  within = c(w), between = c(b), detailed = TRUE
  )
res.aov
get_anova_table(res.aov, correction = "none")
[download]

And after the code change, PDL::Stats now gives the same results as R! If you want to run the above yourself without "installing" any "software", you can enter it in this extremely handy service: https://rdrr.io/snippets/.