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Bayesian t-tests, computing M0 and M1

Dear Bayes factor experts,

Bayesian t-tests in JASP are done following Rouder et al. (2011). For my current purpose I need the separate values of the nominator and denominator of their equation 1:

B01 = (1 + t^2/v)^-(v+1)/2 / ∫ 0- ∞ (1 + Ng)^-1/2(1 + t^2/(1 + Ng)v)^-(v+1)/2 (2 π )^-1/2 g^-3/2 e ^-1/(2g) dg

So, separately the values of the bold and normal parts of their equation, in other words the values of the marginal likelihoods M0 and M1 (if I understood correctly) with only the t-statistic and N available.

Is there any way - either using JASP or e.g. R - to get these values?

Any help is highly appreciated.

ref: Rouder, J. N., Speckman, P. L., Sun, D., Morey, R. D., & Iverson, G. (2009). Bayesian t tests for accepting and rejecting the null hypothesis. Psychonomic bulletin & review16(2), 225-237.

• Hi roundcircle,

Well, you have B01 (from R or JASP), and you can easily compute the numerator, so that then determines the denominator. However, (I have not checked this) I'd be surprised if that equation shows the two marginal likelihoods -- I suspect that common terms will have canceled. An in-depth treatment is available here: http://www.ejwagenmakers.com/2016/LyEtAl2016JMP.pdf (see Eq 10c, that includes additional terms).

Cheers,

E.J.

• Dear EJ,

Thank you for pointing this out! In the meantime I have found a Matlab package that incorporated the formula in one of its functions:

Indeed I could have done it your way, but I was using these terms to show how B01 reacts to changes in t-statistic or N factor. Taking the B01 to compute the denominator would make my argument kind of circular. If any useful literature comes to mind regarding this subject, please post!