Howdy, Stranger!

It looks like you're new here. If you want to get involved, click one of these buttons!

Supported by

Testing assumptions for Bayesian Repeated Measure ANOVA

Dear E.J. plus everyone in the forum,

If I run the classical RM ANOVA in SPSS, by default it produces a table of Mauchley's Test for Sphericity, thus allowing one to check for assumptions and where it is violated, to apply Greenhouse-Geisser corrections for instance. When I run Bayesian RM Anova in JASP, I do not get this assumption displayed in the output and there is no option for checking this assumption. My question is, does Bayesian RM Anova make assumption for sphericity? If it does, how can this be tested? Secondly, does it make assumptions for normality? It will be interesting to point out what assumptions are there for using Bayesian tests (e.g., ANOVA, T-test, etc..). My colleagues have asked me including my students and I have no answer for this or where to refer them to. I truly love JASP an have been encouraging them to use Bayesian statistics as opposed to frequentist statistics.

Thanks for your response.



  • Hi Tom,

    The Bayesian ANOVA (it is really a linear mixed model, see the BayesFactor documentation) makes the same assumptions as the classical ANOVA. We just have not developed the Bayesian echoes for those assumption tests (yet). We will do this in the future, but until that's done you can take a pragmatic approach and use the frequentist tests. There is of course an immediate practical problem -- suppose you do want to correct, how would you do it? In the Bayesian framework, instead of issuing a correction you would apply a more complicated model that can account for the misspecification. But that is work for the future. In general, we hope to give the Bayesian ANOVA some more love in the future.


  • Dear E.J.,

    Many thanks for responding quick to my questions. Much appreciated. I have noted all that you said and will do as suggested. Please one other question: in terms of reporting effect size for the Bayesian ANOVA, how do I go about this? I know for the classical ANOVA, you can obtain partial eta squared, which is also an option in JASP when using the classical RM ANOVA. Lastly, the advanced options for the prior, do I leave the default values as they are or do I have to alter them? I understand the complexities with setting priors and that JASP uses default priors. And what do these represent: r-scale fixed effect, r-scale random effects, r-scale covariates?

    Thank you once again as I look forward to hearing from you.



  • Re effect size: this is not straightforward (I think). There's a paper with Maarten Marsman that is currently somewhere in the review system. We need to polish the Bayesian ANOVA anyway in order to show parameter estimates. We'll take the effect size issue on board then as well. For now, I'd just report the frequentist effect size measure.
    Re priors for ANOVA: I'd leave them as is. The r-scales refer to the width of the prior distribution on the relevant effects. You can check the Rouder and Morey 2012 JMP paper if you feel brave enough. Maybe the BayesFactor documentation offers help as well.

  • Dear JASP/BayesFactor experts,

    I would like to switch from NHST and p values to Bayesian analysis and BFs. In this endeavour I encountered very similar questions like TooFred. I'm fairly new to JASP/BayesFactor.

    How do I test and possibly correct for violations of the test assumptions of Bayesian rm-ANOVA? According to the "Guide for Students" (Mark Goss-Sampson wit van Doorn and EJ) the assumptions are:

    a) DV and residuals should be approximately Gaussian.

    b) No outliers.

    c) Variance homogeneity across factor levels.

    Two questions regarding this:

    1. JASP offers a visual test of normality by providing a QQ-plot. How would I test for variance homogeneity? Would I have to use an old-fashioned frequentist Levene test or F test?
    2. What about sphericity? As far as I know, frequentist rm-ANOVA has some robustness against violations of normality assumptions. Sphericity violations, however, are said to lead to way too liberal statistical decisions. Is this assumption missing in the documentation? Because it is not the same as c).

    To follow up on TooFred's question, I would be curious to learn if the JASPers/BFers have made progress on ways to correct for sphericity violations given what EJ wrote two years ago :) In my experience sphericity violations are more the rule rather than the exception in "real-life" research.

    So it would really be a pity if I were forced to resort to NHST just because they have Greenhouse-Geisser or Huynh-Feldt corrections for such violations while the validity of Bayesian statistical models remains limited to tutorial data (or factorial designs with only binary factors - which is already good! Just quite a limitation.)

    Is it still recommended to check for sphericity using Mauchly's test (or - alternatively - calculate GG's epsilon) and to switch back to NHST if needed? Wouldn't for instance a Bayesian Friedman test be a promising alternative in this scenario, which currently is not available in JASP?

    Thanks & best,


  • Hi Michael,

    Yes we made some progress (e.g.,, but this has not yet resulted in changes to JASP, unfortunately. I do think it's important to be able to do ALL analyses within the Bayesian paradigm, so I'll bump this on our priority list.



  • Dear E.J., dear JASPers,

    OK, sounds great! From having a brief look at it, it seems that the proposed method would extend JASP in that it provides a test for checking assumption c) that I mentioned above. At present I'm checking this using Levene's test. The Q-Q plot takes care of assumption a). (FYI: I am referring to the assumptions as mentioned in this manual on page 90.)

    If I understand correctly though, the new paper you mentioned does not test/correct for sphericity violations, an assumption that is not mentioned in the accompanying documentation.

    It has been my understanding that variance homogeneity across conditions was an assumption of (classical) ANOVA with only between-subject factors and that due to the nature of repeated-measures ANOVA this assumption turns into the sphericity assumption (commonly tested with Mauchly's test), which concerns the homogeneity of variances across condition differences.

    Perhaps my point doesn't even really affect JASP per se but rather the author of that manual: this sphericity assumption does not even show up there.



  • Dear all,

    I am currently facing a similar problem as TooFred.

    I did a Bayes rmANOVA in JASP with 2 within-subject factors and tested the assumption of sphericity with the frequentist approach.

    Unfortunately, the assumption is violated.

    Do somebody know how I can correct it/apply another model?

    Thanks in advance!


  • It seems to me that if researchers are to report frequentist effect sizes to go along with their Bayesian 'repeated measures' analysis, those effect sizes should not come from a frequentist repeated-measures ANOVA. Instead, they should come from a frequentist linear mixed model. This is because the data on which the Bayesian "repeated-measures" ANOVA are based may be different than the data on which the frequentist repeated-measures ANOVA are based: The frequentist repeated-measures ANOVA will automatically drop participants with incomplete data, whereas the Bayesian "repeated-measures" ANOVA and the frequentist mixed linear model will not drop participants with incomplete data.


Sign In or Register to comment.

agen judi bola , sportbook, casino, togel, number game, singapore, tangkas, basket, slot, poker, dominoqq, agen bola. Semua permainan bisa dimainkan hanya dengan 1 ID. minimal deposit 50.000 ,- bonus cashback hingga 10% , diskon togel hingga 66% bisa bermain di android dan IOS kapanpun dan dimana pun. poker , bandarq , aduq, domino qq , dominobet. Semua permainan bisa dimainkan hanya dengan 1 ID. minimal deposit 10.000 ,- bonus turnover 0.5% dan bonus referral 20%. Bonus - bonus yang dihadirkan bisa terbilang cukup tinggi dan memuaskan, anda hanya perlu memasang pada situs yang memberikan bursa pasaran terbaik yaitu Bola168. Situs penyedia segala jenis permainan poker online kini semakin banyak ditemukan di Internet, salah satunya TahunQQ merupakan situs Agen Judi Domino66 Dan BandarQ Terpercaya yang mampu memberikan banyak provit bagi bettornya. Permainan Yang Di Sediakan Dewi365 Juga sangat banyak Dan menarik dan Peluang untuk memenangkan Taruhan Judi online ini juga sangat mudah . Mainkan Segera Taruhan Sportbook anda bersama Agen Judi Bola Bersama Dewi365 Kemenangan Anda Berapa pun akan Terbayarkan. Tersedia 9 macam permainan seru yang bisa kamu mainkan hanya di dalam 1 ID saja. Permainan seru yang tersedia seperti Poker, Domino QQ Dan juga BandarQ Online. Semuanya tersedia lengkap hanya di ABGQQ. Situs ABGQQ sangat mudah dimenangkan, kamu juga akan mendapatkan mega bonus dan setiap pemain berhak mendapatkan cashback mingguan. ABGQQ juga telah diakui sebagai Bandar Domino Online yang menjamin sistem FAIR PLAY disetiap permainan yang bisa dimainkan dengan deposit minimal hanya Rp.25.000. DEWI365 adalah Bandar Judi Bola Terpercaya & resmi dan terpercaya di indonesia. Situs judi bola ini menyediakan fasilitas bagi anda untuk dapat bermain memainkan permainan judi bola. Didalam situs ini memiliki berbagai permainan taruhan bola terlengkap seperti Sbobet, yang membuat DEWI365 menjadi situs judi bola terbaik dan terpercaya di Indonesia. Tentunya sebagai situs yang bertugas sebagai Bandar Poker Online pastinya akan berusaha untuk menjaga semua informasi dan keamanan yang terdapat di POKERQQ13. Kotakqq adalah situs Judi Poker Online Terpercayayang menyediakan 9 jenis permainan sakong online, dominoqq, domino99, bandarq, bandar ceme, aduq, poker online, bandar poker, balak66, perang baccarat, dan capsa susun. Dengan minimal deposit withdraw 15.000 Anda sudah bisa memainkan semua permaina pkv games di situs kami. Jackpot besar,Win rate tinggi, Fair play, PKV Games