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# Confidence intervals and one-wayd hypotheses for correlations

Hi!

I have two questions:

1) When I do Bayesian tests for correlations and get a confidence interval in JASP - is that a confidence interval for the effect size or for the correlation?

2) When changing my hypothesis to be one-way (in a certain direction), the confidence interval also changes. Would it, for this reason, be better to do a two-way test instead, so that I get a confidence interval that better represents what the confidence interval looks like in the population? Like, even if I expect the correlation to go in a certain direction, wouldn't the confidence interval for the non-directed hypothesis give me the best approximation of what the effect actually looks like "in the population"? Like, should the outcome really change based on if my expectation change? I mean, my expectation could be terrible...

• If you're using R, you can get a posterior CI based on the null + two tailed + one tailed (all weighted based on the BF). You can read more about why you should do this here: https://doi.org/10.31234/osf.io/h6pr8

Here is an example using `BayesFactor` and `bayestestR`:

`library(BayesFactor)`

`library(bayestestR)`

`corr_BF_two_tailed <- correlationBF(iris\$Sepal.Width, iris\$Sepal.Length)`

`corr_BF_left_tailed <- correlationBF(iris\$Sepal.Width, iris\$Sepal.Length,`

`                   nullInterval = c(-1, 0))[1]`

`corr_BF <- c(corr_BF_two_tailed, corr_BF_left_tailed)`

`post_w <- weighted_posteriors(corr_BF)`

`#> Independent-candidate M-H acceptance rate: 96%`

`#> Independent-candidate M-H acceptance rate: 100%`

`hist(post_w\$rho)`

`describe_posterior(post_w\$rho)`

`#> # Description of Posterior Distributions`

`#> `

`#> Parameter | Median |          89% CI |    pd |        89% ROPE | % in ROPE`

`#> --------------------------------------------------------------------------`

`#> Posterior | -0.047 | [-0.202, 0.000] | 0.572 | [-0.100, 0.100] |  69.483`

• "1) When I do Bayesian tests for correlations and get a confidence interval in JASP - is that a confidence interval for the effect size or for the correlation?"

For the correlation.

"2) When changing my hypothesis to be one-way (in a certain direction), the confidence interval also changes. Would it, for this reason, be better to do a two-way test instead, so that I get a confidence interval that better represents what the confidence interval looks like in the population?"

We generally recommend one-sided tests but two-sided credible intervals. See https://psyarxiv.com/yqxfr

E.J.

• "1) Great, thanks!

"2) Yes that makes perfect sense, a little embarrassed I didn't think of that myself :)