Hello! In this video I compute and report results for comparable frequentist and Bayesian independent samples t-tests. The data is available on Kaggle: www.kaggle.com/datasets/mukes...
A Cauchy prior with a scale of r = .707 is the default prior in JASP for t-tests. The Cauchy distribution is like a univariate normal distribution, but it has heavier tails (the dashed line in the figure). The prior of the effect size (what we know before observing data) is centered at zero. The null hypothesis predicts an effect size of 0 (difference in means over the pooled standard deviation) and the alternative hypothesis predicts effect size of 0 with an interquartile range of -.707 to .707 (see Wagenmakers et al., 2018). Thus, as the effect size grows larger, the evidence suggests that the alternative hypothesis is better at explaining the data. Also check out these resources! forum.cogsci.nl/discussion/3236/setting-cauchy-prior-scaling-in-bayesian-t-test-use-related-effect-size osf.io/ahhdr/download
Info is sparse, but it looks like the mean (location) for an informed prior is the effect size, and the sd (scale) would be the pooled standard deviation. I'll keep looking around to confirm, but any info on that issue would be massively appreciated!
The location parameter specifies the effect size and the scale parameter specifies the width of the distribution. When the scale parameter is .707, we can interpret this to mean that "We are 50% confident that the effect size is between d = -.707 and d = .707" (Schmalz et al., 2021, p. 7). In other words, the scale parameter is specifying the bounds of what is likely with a 50% probability. Schmalz et al. (2021) psycnet.apa.org/fulltext/2022-03331-001.pdf
