Sample Size - GPower options in F tests, ANOVA: Repeated measures, within factors I'm trying to determine sample size and found that the "Options" in G*Power 3.1.9.7 changes the effect size (seems to automatically convert this and provides the same results, first two pictures). Once I change the f(V) to 0.1 (for small effect size the sample size increased a lot, third picture).
The default one is not the recommended one which is confusing. Can anyone point to what the different effect size versions mean or when they should be used?

*

*"f" for GPower 3.0

*"f(U)" for SPSS

*"f(V)" for Cohen (1988), it notes
that this is recommended, but this isn't the default. It is the method used in WebPower
Effect size specification GPower: 
Effect size specification Cohen converted:
Effect size specification Cohen unconverted: 
 A: The documents here: https://www.psychologie.hhu.de/arbeitsgruppen/allgemeine-psychologie-und-arbeitspsychologie/gpower
may be read to see what the option "as in G*Power 3.0" does.
This huge difference between the "as in G*Power 3.0" (having a much larger value  of the required sample size) and the other options for the within-between interaction has been noted elsewhere (see, for example, here: https://vdocument.in/rnr-based-assessment-feedback-reception-by-offenders-and-2014-09-05-vii-abstract.html?page=1), and I see it also holds for the "within" effect (giving the same results).
There are discussions about that here: https://www.facebook.com/groups/853552931365745/posts/1670186976368999/
and here: https://www.researchgate.net/post/Why_GPower_and_MorePower_are_calculating_different_sample_sizes .
Both discussions quote this paper:
https://www.frontiersin.org/articles/10.3389/fpsyg.2013.00863/full
that explains that:

*

*"f(U)" for SPSS and "f(V)" for Cohen (1988) are very similar. They actually vary based on how the non-centrality parameter is calculated
(the point being whether the sample size or the degrees of freedom are used);


*as you noticed, the "f" for GPower 3.0 is very different. This is because correlation is not incorporated directly, but it is part of the formula (thus, it must be explicitely defined, because it is necessary to calculate the non-centrality parameter). The formula is shown in the paper's Appendix.
While, for the "between" variance, it seems to me the other options are extremely conservative, basically corresponding to a correlation as close to 1 as possible (after running different effect sizes, I would say it typically is 0.9999), for the "within" and the "interaction" effect the issue (a personal communication with one of the G*Power developers confirmed it) is the one described here: GPower: Difference in Sample Size for ANCOVA vs. Repeated Measures ANOVA in clinical trials
i.e. the quantity at denominator: if I well understand, in the case of the interaction effect, the use of the error variance (in the default option, requiring thus explicit specification of the correlation to calculate the ES) vs the "between-within" error variance (in the other options, incorporating both the error variance and the correlation). The same reasoning applies to the "within" effect (in that case, it is the within-subject error variance that is used by the non-default options).
The automatic conversion of the ES you notice in order to keep the required sample size constant occurs not only with the "as in Cohen", but also with the "as in SPSS" option. Here: https://aaroncaldwell.us/SuperpowerBook/repeated-measures-anova.html, in Section 4.2.2, the issue is presented in this way: "We click the ‘Options’ button, and check the radio button next to ‘As in SPSS.’ Click ok, and you will notice that the ‘Corr among rep measures’ field has disappeared. The correlation does not need to be entered seperately, but is incorporated in Cohen’s f. The value of Cohen’s f, which was 0.25, has changed into 0.7024394. This is the SPSS equivalent".
