Using G*Power: I have mixed ANOVA with 2 within-subjects factors and 3 between-subjects factors
I chose F test: ANOVA, repeated measures, within-between interaction -> I don't know how this is different from repeated measures, between factors?
alpha= 0.05 power= 0.80 number of groups= 3 number of measurements= 2 correlation among repeated measures= I don't know how to determine this, but I relied on the default value of 0.5??
nonsphericity correction error= I don't know how to determine this either, but I relied on the default value of 1?
the total sample size I got was 42, isn't this value too low? And since there are 3 groups, does this mean I need at least 42/3= 14 participants in each group? N= 42 seems very low thank you !
Mehmet Sinan Iyisoy, thanks for the video. A quick perusal suggests that it is relatively well done; with some caveats, it could be useful form my students.
However, as far as I saw, it didn't address the "Nonsphericity correction epsilon" (wish we had Greek characters here), so, as Franklin Li specifically mentioned it, I thought that I might clarify.
Sphericity is an assumption of repeated measures univariate ANOVA. As such, after data collection, we typically test that assumption with Mauchly's test, and it might be noted that RM ANOVA is not particularly robust to violations of this assumption. If the null hypothesis of sphericity is rejected, then, if we wish to remain with a univariate ANOVA analysis, we can calculate an index, usually referred to as "epsilon" that decreases monotonically from 1.0 with the degree to which our data are not spherical, or one might say "nonspherical." [This gets even more complicated here as there is more than one formula to calculate epsilon; I use that due to Greenhouse and Geisser.] The way this "modified" ANOVA works is to reduce the numerator and denominator dfs by multiplying them by this index. Of course, this changes the power of the ANOVA, and this is what GPower is looking for, so it can know whether the dfs will be reduced. As with all a priori power analyses, there is information that we do not have, and can only guess at; this would, of course, be such information. If a study of the same ilk has been conducted before, that might offer guidance. It is an interesting situation though, as there would only be a reduction in dfs if Mauchly's test is significant. If that does not obtain, then, even if the epsilon is substantially < 1, there would still be no reduction, and the power would be the same as if epsilon was "1.0."
On the other hand, there is another alternative, and is why I continued to say "univariate" above. One can pursue this from a multivariate perspective, and adapt Hotelling's T2 to this purpose. Hotelling's T2 does not assume sphericity, therefore the potential deleterious effect of "nonsphericity" on Type I error is obviated; unfortunately, the expected Type II error may be such that power is lost with this decision. I use my on code for this, but I do know that SPSS offers both univariate and multivariate output.
My best to your research,
John
John Morris Thank you very much for your informative response and also thank you Mehmet Sinan Iyisoy for your resource recommendation
to conduct a mixed ANOVA, in G*Power, which option do I select:
repeated measures between factors,
repeated measures within factors,
or repeated measures within-between interaction?
I have 2 within-subjects factors and 3 between-subjects factors
Thanks!
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