3
$\begingroup$

Recently a paper indicated a method to calculate Bayes Factor for correlations (http://link.springer.com/article/10.3758/s13423-012-0295-x/fulltext.html). This method doesn't use significance testing as is typical to decide if a correlation is noteworthy*. My question is, if one uses Bayes factor as a method of evaluating correlations*, is there still a concern of alpha inflation/familywise error rate?

*I understand that one is really testing the null hypothesis that the correlation strength is equal to 0 and purposefully didn't go into that so the question is more clear.

$\endgroup$

1 Answer 1

3
$\begingroup$

Alpha inflation and familywise error is not an issue if the math was done properly with regard to the Bayesian posterior density function. For binary hypotheses Bayes factors and the Bayesian posterior work the same way, but for non-binary hypotheses, Bayes factors can pick up many of the same problems as p-values, though not familywise error rates or alpha inflation in particular.

There is no concept of chance in Bayesian methods, only uncertainty. There is no null hypothesis in Bayesian methods. No hypothesis is assumed to be true. While I would not be hesitant to use a posterior density to evaluate a correlation, I might have concerns about Bayes factors unless the hypothesis was binary. While Bayes factors are nice in that they avoid the issue of the prior density, that very avoidance imbues Bayes factors the same problems p-values can have.

Additionally, Bayesian hypotheses are combinatoric. There should be one hypothesis for each possible combination of variables. These are not separate tests, but rather one large joint test. Unlike a master F-test which asks if all variables are uncorrelated, the Bayesian posterior is the probability each hypothesis is true.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.