Confidence intervals and one-wayd hypotheses for correlations

Comments

• MSB

  July 2020

  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

  July 2020

  "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

  July 2020

  "1) Great, thanks!

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