# Solutions for non parametric bayesian RM ANOVA ?

Hello everyone,

Simple question: There is a way somewhere to perform a non parametric Bayesian Repeated Measures ANOVA ?

The only solution I found for the moment is to rank transform my DV and then to performed classical parametric analyses (in bayesian or not). Nonetheless, I'm not very happy with data transformation.

Any comments would be very appreciate,

Thanks,

Guillaume

## Comments

Hi Guillaume,

Ah, but nonparametrics is a little more tricky with Bayes, as it inverts a generative model. The rank transform will produce OK result but only with large N (from a Bayesian perspective). Anyway, perhaps this is of interest: http://georgek.people.uic.edu/BayesSoftware.html

Cheers,

E.J.

Thanks EJ for your response and the software, I will check,

As you are here : )

You tell me that the rank transformation is OK with a "large N from a Bayesian perspective". So what do you mean by large N ? : )

I already asked the question on researchgate (regarding the impact of the sample size on bayes factors), peoples kindly send me some articles, however I don't understand it...

Thanks again,

Suppose you compute a Spearman's rho and conduct the standard analysis on the ranks. Suppose you have three observations, and the ranks are the same in the two variables. This yields:

X Y

1.00000... 1.00000... (rank 1 for X and Y)

2.00000... 2.00000... (rank 2 for X and Y)

3.00000... 3.00000... (rank 3 for X and Y)

If you mistakenly assume the data are continuous, the BFfor this small data set will be infinite (as the method will conclude there is no measurement noise). As you see more ranks (N increases) this problem will lessen. Of course it is much better to take into account that the data are in fact ranks and not continuous.

Cheers,

E.J.

Thanks EJ,

I will update the discussion rapidly (I hope),

Best

Just for the news,

I have finally transformed two of of my DV and I have conduct a Bayesian RM ANOVA on,

The results are similar across different transformations and models (e.g., GLM poison distribution),

Thanks EJ,

Best,