Reporting posterior R² and posterior effect size in Bayesian rmANOVA and paired t-tests

johan_achard

Dear JASP team,

I am using Bayesian repeated-measures ANOVAs and Bayesian paired-samples t-tests in JASP and would like to clarify how best to report effect sizes and uncertainty measures within a Bayesian framework.

For the Bayesian repeated-measures ANOVA, JASP provides a “Posterior R²”, described as the posterior distribution of explained variance. I am considering reporting the model-averaged posterior R² together with its 95% credible interval as a model-level measure of effect size/uncertainty.

I would like to clarify a few points:

• What exactly does the model-averaged posterior R² correspond to in Bayesian repeated-measures ANOVA? Is it the proportion of variance explained by the fixed effects, by the full model including random factors, or by the model-averaged set of models weighted by posterior model probabilities?
• Should posterior R² be interpreted as a model-level measure of explained variance rather than as an effect size for a specific factor?
• JASP seems to summarize posterior R² using a posterior mean and 95% credible interval, whereas Bayesian paired-samples t-tests report the posterior median of the standardized effect size δ with a 95% credible interval. Would it be possible to obtain and report either the posterior mean or the posterior median for both quantities? Reporting a posterior mean for R² and a posterior median for δ seems somewhat inconsistent, and I wonder whether a common summary statistic would be preferable for coherent reporting.

Many thanks for your help and clarifications !

Johan

EJ

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EJ