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Using R! Here is an example: www.r-bloggers.com/2019/07/integration-in-r/

Standard error is computed by dividing the standard deviation by the square root of n. In this case, the standard error of "Less than 20" would be 3.05/sqrt(1819) = .07. Thus you would need to divide the "CI_Diff/2" column by 2 to get the standard error.

@@karyssa_ Much obliged

Yes, they are just charlatans with a degree. But you can earn money scamming people.

Yes! The BayesFactor package in R can compute BFs, other packages have BF functions as well (e.g., packages built on stan such as brms).

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

@@karyssa_ Thank you very much!

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

Thank you!

Glad it was helpful!

It's hard to address your specific problem without seeing your analysis, but I would guess that the informed prior added information making the posterior estimation more certain in the parameter estimate (and thus credible intervals narrower). When the prior is non-informative, the posterior is much more similar to likelihood (because the posterior is a compromise between the prior and the likelihood). It's possible that the informed prior centered on a smaller effect size, causing the posterior effect size to be smaller compared to the analysis with a non-informed prior.