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If you're working with crossed random effects (a sample of words and a sample of people), you should report a minF' rather than just your F1 and F2 values according to Clark (1973), Raaijmakers et al. (1999), ...

I've found this site which calculates the minF' for me. However, this only works if my degrees of freedom for F1 and F2 are the same. Since the assumption of sphericity was violated in my F1 analysis, I used a Greenhouse-Geisser correction, which resulted in different degrees of freedom.

How can I calculate a minF' in this case? Or do the degrees of freedom not play a role, given an F-statistic? This is possible, since the original formula only worked with the F-statistics. Is there a site or a piece of software (similar to the one I linked) that can do this?

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Mixed effect, or multi-level, modelling is the answer here. The Min F' calculation option is exactly the kind of thing obviated by such a technique. You'll want to read Baayen 2008 (pdf of final draft available from the author), especially chapter 7. It directly addresses the same field of research as you're discussing.

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  • $\begingroup$ Yes, I know of mixed effects models, but I wanted to try the old method for fun. $\endgroup$
    – Mien
    Commented Jun 24, 2012 at 7:20
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The problem you'll have here is that each of your F's is calculated across different terms and therefore really has different underlying effect variances and different violations of sphericity. A violation on the treatment effect doesn't mean you have a violation on the words. Unless you recalculate sphericity for your specific terms leading to your Fmin' you're not going to solve this.

There isn't a calculator out that that does this for you.

On the bright side, people have pretty much ignored the sphericity assumption for many decades. Perhaps you can as well. The degree of violation is a random variable, if you haven't violated it by much then perhaps you haven't really violated it. Furthermore, the G-G and H-F corrections don't solve the problem, they just ameliorate it (sometimes). It's possible to over correct and go from Type I to Type II errors, or not quite correct enough. Some argue you only use the epsilons as an indicator of whether you should even trust the ANOVA at all, not just to correct the F's.

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  • $\begingroup$ Well, my F1 statistic was the same with or without correction, so the F' statistic didn't change. I wasn't able to double-check the corresponding p-value though. By now, I've found out that I didn't even need a F2 analysis (nor a minF') in my case, since the items weren't nested in the treatment. But thanks for your input, it's appreciated! $\endgroup$
    – Mien
    Commented Jun 24, 2012 at 14:21

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