mjskay
wrong formula for mixed designs?
I don't know if you have seen this paper: https://journal.r-project.org/archive/2016/RJ-2016-027/RJ-2016-027.pdf
On page 376, it states: "This indicates that the art function from ARTool uses the wrong Higgins and Tashtoush formula for aligning the data in mixed designs. It uses the formula for between x between designs, instead of using the formula for mixed (In Higgins’s terms: split-plot or repeated measures) designs."
I did not test this myself, but I was wondering whether you can confirm this as a potential issue? Thanks!
Hmm, I had not seen that paper, thanks for raising this. The alignment process implemented in the R version of ARTool is the same as the alignment process implemented in the original ARTool software from Wobbrock & Higgins et al., which is that for a completely randomized design. According to that page:
The alignment process used is that for a completely randomized design. This can result in reduced power for other designs like split-plots, as described in Higgins et al. (1990). But this is the simplest and most easily generalized alignment algorithm to implement. As it may only reduce power, any significant results can be trusted. For more on this issue, see Higgins et al. (1990) and Higgins & Tashtoush (1994).
At the very least, this is worth raising a warning or a note in the docs. If I have more time I might look into implementing the more specific algorithms for alignment of other designs.
