How the Bayesia paired t-test is applied
Hi, recently I received a question from a reviewer asking how the Bayesian paired t-test is applied. I assume the question refers to the assumption behind the testing. So what are the assumptions? I am not sure if the ones described in the JASP refer to the NHST or Bayesian approach (continuous difference score; The difference scores are a random sample from the population; The difference scores are normally distributed in the population).
I found that the Bayesian t-test was developed by Kruschke (Bayesian estimation alternative to the t-test - Bayesian Estimation Supersedes the T-test; BEST). However, the assumptions behind the BEST are different (e.g. t-distribution rather than normal) from the NHST t-test ones.
Would anyone be able to assist? (have to submit the rebuttal letter in a few days).
thanks
Comments
In any t test, the theoretical, sampling distribution of t scores is distributed according to a t distribution, not a normal distribution. It is the population(s) of raw scores, from which the data scores are sampled, that are assumed to be normally distributed.
R
Kruschke developed a Bayesian t-test (with the emphasis on "a"). This is not the one implemented in JASP, which is based on the work by Jeffreys. In the help file you will see a reference to Rouder et al., 2009, and Gronau et al.
The assumptions of Jeffreys's t-test are exactly the same as for the regular, classical t-test.
Indeed, Kruschke's test assumes that the data are t-distributed instead of normally distributed. This is an interesting approach, but not the standard one, and not the one that is currently implemented in JASP.
Cheers,
E.J.
Thank you E.J.!