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I'm conducting a two-way ANOVA with one within-subjects factor A (A1; A2) and one between-subjects factor B (B1; B2), but I would like conduct this with the bayesian approach. I did it with JASP.

However, is it possible to compute simple main effect for Bayesian ANOVA ? If yes, how can I do it ? This option is not available in JASP, thus can I do it with t-test, as it's possible in frequentist approach when interaction is significant ? Or, is it possible to do it with R ?

Moreover, I computed bayesian post-hoc in JASP and BF were the same than Bayesian t-test... So I did not understand why...

Finally, my last question is about power. I don't have many participants, so how to know if my bayesian analysis did not suffer from a lack of power when BF shows anecdotical evidence ?

I have read this article on the topic but did not find an answer :

Jong, Marsman, Wagenmakers (2019)

Bergh, D. Van Den, Doorn, J. Van, Marsman, M., Draws, T., van Kesteren, E.-J., Derks, K., … Wagenmakers, E. J. (2019). A Tutorial on Conducting and Interpreting a Bayesian ANOVA in JASP. 1–22. doi:10.31234/osf.io/spreb

Rouder, J. N., Engelhardt, C. R., McCabe, S., & Morey, R. D. (2016). Model comparison in ANOVA. Psychonomic Bulletin and Review, 23(6), 1779–1786. doi:10.3758/s13423-016-1026-5

Thanks for your answer,

PM

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Welcome to stackexchange.

However, is it possible to compute simple main effect for Bayesian ANOVA ? If yes, how can I do it ? This option is not available in JASP, thus can I do it with t-test, as it's possible in frequentist approach when interaction is significant ? Or, is it possible to do it with R ?

Moreover, I computed bayesian post-hoc in JASP and BF were the same than Bayesian t-test... So I did not understand why...

The simple main effects in your design capture the difference between A1 and A2, or between B1 and B2. These should already available in the ANOVA input of any program, including JASP.

Finally, my last question is about power. I don't have many participants, so how to know if my bayesian analysis did not suffer from a lack of power when BF shows anecdotical evidence ?

Power is a frequentist concept, and does not play a role in Bayesian statistics. However, you can answer your question quite easily in Bayesian statistics: if the BF indicates only anecdotal evidence in either direction (in favour of the null hypothesis, or in favour of the alternative), this means you don't have enough data to be sure that there is an effect, and you don't have enough data to be sure that there isn't an effect.

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  • $\begingroup$ Thank your for your answer ! OK for statistical power. However about simple main effect, my purpose is to assess effect of A (i.e., difference between A1 and A2) B1 and B2. Post-hoc allow to capture difference between A1 and A2, as well as B1 and B2. But it is an analysis of main effect. I would like analysis interaction effect. $\endgroup$
    – PM_cog
    Commented Apr 10, 2020 at 12:50
  • $\begingroup$ I'm sorry, I don't understand your question in that case. Could you please try to explain what it is you actually want to calculate? The main effect? Simple effects (e.g. A1.B1 - A1.B2)? Interactions? $\endgroup$
    – Eoin
    Commented Apr 10, 2020 at 12:54
  • $\begingroup$ I would like calculate bayesian simple effects. $\endgroup$
    – PM_cog
    Commented Apr 10, 2020 at 13:02
  • $\begingroup$ Then use a (Bayesian) t-test to compare each pair of groups (e.g. A1.B1 - A1.B2). $\endgroup$
    – Eoin
    Commented Apr 10, 2020 at 13:05
  • $\begingroup$ Great ! Are there conditions (e.g., minimal BF for interaction) or precautions (e.g., correction) to use multiple t-test in this case ? I mean, if there are not conditions or precautions why use ANOVA and not directly use multiple t-test ? $\endgroup$
    – PM_cog
    Commented Apr 10, 2020 at 13:11

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