Home forums ANOVA Default Sphericity correction method: GG?

This topic contains 2 replies, has 2 voices, and was last updated by  LIU Lei 4 months, 3 weeks ago.

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  • #363

    LIU Lei
    Participant

    Why the Default results of RMANOVA are corrected by GG? The textbook and wikipedia told us that when the results of Mauchly Tests for Sphericity is not significant, there ‘s no need for correction. When the results of Mauchly Tests for Sphericity is significant, we should choice the the correction method according to epsilon.

  • #364

    henrik
    Keymaster

    The reason I have not implemented the approach you suggest is because I believe it is not statistically fully appropriate. Specifically, the Mauchly test, as any significance test, has a specific power and Type I error rate (the latter of which is controlled by the alpha/significance level). I do not believe it is worthwhile to incorporate these additional error probabilities into an analysis. Instead, I believe that the small loss in power by always using Greenhouse-Geisser is overall a more appropriate strategy and more conservative.

    Consider the case in which the Mauchly test fails to correctly detect a violation because the power is too low in a specific case. If this happens, you get inflated Type I error rates. I consider this a potentially larger drawback than occasionally committing a Type II error in case Greenhouse-Geisser is too strict.

    I believe that in general, significance tests for testing assumptions is not a good idea. For some arguments why see:
    https://stats.stackexchange.com/q/2824/442
    https://stats.stackexchange.com/q/2492/442

    Nevertheless, the current development version of afex now makes it easier to get assumption tests, see:
    https://github.com/singmann/afex/pull/69

  • #367

    LIU Lei
    Participant

    Great, thank you so much. You know some editors and reviewers take the traditional methods as the golden standard.

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