Confidence intervals and one-wayd hypotheses for correlations

perdavidson

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...

MSB

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

EJ

"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.

perdavidson

"1) Great, thanks!

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