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// Reporting Mixed ANOVA - results from SPSS //

Reporting the mixed ANOVA will give you three possible scenarios.

Please keep in mind that if your mixed ANOVA violated the assumption of sphericity, the corrected results (for the within-subject and interaction effect) need to be reported.

1) In case none of your effects is significant, you will report that. Simply provide the F-statistic alongside the degrees of freedom as well as the p-value.

2) In case you have a significant interaction of your between-subject effect and within-subject effect, you will report this and only this.
Be aware though, that some reviewers will still insist on main effects being reported, despite them being rendered kind of useless when the interaction effect turned out to be significant.

3) In case your interaction effect is not significant, you will report main effects, regardless of significance or not. Additionally, you will also report the non-significance of the interaction effect.

The effect size, usually eta squared, should also be reported and classified. For classification a transofrmation from Eta-Squared to f is necessary.

Cohen (1988), p. 284 provides the proper formula for that. Use effect sizes from similar studies or research-field-specific thresholds to classify your effect size(s). In case you have neither at your disposal, you can fall back to the thresholds from Cohen (1992).


Sample formulation:
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Scenario 3 from above:
"The mixed ANOVA showed no significance for an interaction
effect (F(Df1, DF2) = F-statistic, p-value).
But both, the between-subject effect (F(1,58) = 21.40, p ◃ 0.001, η2 = .071) and within-subject effect (F(3.28, 190.42) = 3.72, p = 0.01, η2 = .048), showed significant differences."


📚 Literature
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📚 Cohen, J. (1992): Quantitative methods in psychology: A power primer. Psychological bulletin, pp. 155-159.
📚Cohen, J. (1988): Statistical Power Analysis for the Behavioral Sciences.


⏰ Timestamps:
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0:00 Introduction and Scenario I - no significant effects
0:14 Scenario II - significant interaction effect
0:41 Scenario III - non-significant interaction effect
0:58 Effect sizes


If you have any questions or suggestions regarding the write-up for the mixed ANOVA in R, please use the comment function. Thumbs up or down to decide if you found the video helpful.

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