# Effectsize in JASP

Hi All,

So I have been wondering something lately; is it possible to have JASP give you some sort of indicator of the effect for an AN(C)OVA, or t-test? I'm looking for some sort of Bayesian equivalent of partial eta squared or Cohen's d. Would be amazing if there was a paper somewhere with guidelines on how to qualitatively interpret that Bayesian effect size as small, medium or large.

## Comments

We have a paper about effect size for ANOVA (minor revision); For the t-test, the standard output gives the posterior distribution for Cohen's delta (on the population level). The interpretation in terms of what is large won't differ (and depends on context and the purpose of the researcher) between Bayesians and frequentists. However, for a Bayesian the effect size estimates will shrink to zero (depending on the prior and possible hierarchical structure) and it is natural to inspect the entire posterior distribution, which automatically provides an impression of the uncertainty (over and above the point estimates).

E.J.

Dear E.J.,

Thank you for all your useful responses - this is really helping me grasp a lot of fundamentals that are behind the Bayesian approach to data analysis.

I have one question that is sort of related to this post. Do Bayes Factors share the same problem with p-values, in that they both do not tell the researcher much about the size or magnitude of the observable differences (for example, in a t-test) the same way an effect size, d would?

Kind regards,

Michael

Hi Michael,

Correct -- the usual BF involves a null hypothesis and is therefore a test of presence/absence, not one of magnitude.

Cheers,

E.J.

Hi E.J.,

Thanks for your reply. However, as a pragmatic JASP user, I'm not sure how to interpret your answer, or how to report Cohen's Delta as an effect size. Do you think it's possible (in future versions of JASP) to have JASP produce a number as an effect size for a given test. Or am I now requesting something that is impossible?

Kevin

Hi Kevin,

JASP already provides effect sizes. To clarify, for the Bayesian methods JASP generally provides the following:

(1) The Bayes factor, a single number that quantifies the evidence for the presence/absence of an effect;

(2) A posterior distribution, quantifying the uncertainty about the size of the effect under the assumption that it exists (H1). Usually this distribution is summarized by a central tendency (e.g., median) and dispersion (e.g., 95% credible interval).

Cheers,

E.J.

Dear EJ, in t test, the effect size plotted in the prior-post plot is "Cohen's delta" or "Gates'

delta"? ThanksI'm not aware of a Gates' delta.

It's the population mean divided by the population sd, so the population version of Cohen's d (i.e., Cohen's delta).

E.J.