Is this how JASP defines H0, H1, calculates the BF and plots the results ?

pieter

Can someone please confirm if my understanding is right? Or - correct me if I am wrong? Thanks!

I am doing a One Sample Bayesian t-test. Data: 175 cases, sample mean for variable V is 6.59
H0: population mean is 6.0
H1: population mean > 6.0
(in other words, I am testing the hypothesis that δ>0 versus δ=0).

My Questions:

1. HOW IS H0 SPECIFIED? Is H0 a normal distribution, centered on δ=0 ? How is the spread specified (is the standarddeviation of this H0-distribution somehow derived from the _sample _standard deviation ?? That would be strange, because then you inject information from the data into the H0, thus improving the fit between H0 and data...... ?

2. Am I correct in that H1 is the positive portion of the Cauchy distribution, with most mass close to zero. ?

3. My BF10 = P(data|H1) / P(data|H0) So this is a ratio of two p-values, right?

4. In my case BF10 = 23915, suggesting that the data are more supportive of H1 than of H0. But what does the "error %" mean, that is given BF? In my case it is 1.253 e-10 (so very small).

Thanks ! Learning every day... !

EJ

Hi Pieter,

The answers:
1. "HOW IS H0 SPECIFIED?"

H0 is the single point delta=0. So there is no spread. H0 states that the effect is completely and utterly absent.

2. "Am I correct in that H1 is the positive portion of the Cauchy distribution, with most mass close to zero?"

Yes. It is obtained by folding the bell-shaped two-sided Cauchy distribution around 0.

3. "My BF10 = P(data|H1) / P(data|H0) So this is a ratio of two p-values, right?"

Not quite. For instance, the p-value is not the probability of the data, but the probability of encountering a test statistic at least as extreme as the one you've observed. There are other differences as well, but basically, the p-value is a tail area integral. The Bayes factor is a (generalized form of) likelihood ratio.

4. "In my case BF10 = 23915, suggesting that the data are more supportive of H1 than of H0. But what does the "error %" mean, that is given BF? In my case it is 1.253 e-10 (so very small)."

"Suggesting" is rather too modest -- the data provide overwhelming support and are 23,915 times more likely under H1 than under H0! The error percentage is there because the result requires some numerical integration. I forgot what it does exactly...let me check.

Cheers,
E.J.

pieter

Thank you EJ. Guess I will dive into some papers on BF to learn.more.