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# One-sided Bayesian t test with the BayesFactor package - How to get posterior of d?

Hi,

I am trying to replicate the one-sided Bayesian t test from JASP with the BayesFactor package in R. To get the posterior of d, I use:
bf <- ttestBF(formula = Variable1 ~ Variable2, data = mydata)
bf
chains = posterior(bf, iterations = 1000000)
summary(chains)
median(chains[,4])

This gives me the median of the posterior of the effect size, right?
However, if I use a one-sided test:
bf.signed = ttestBF(formula = Variable1 ~ Variable2, data = mydata, nullInterval = c(Inf, 0))
bf.signed
chains = posterior(bf.signed, iterations = 1000000)
summary(chains)
median(chains[,4])

R produces the following error:

chains = posterior(bf.signed, iterations = 1000000)

Error in posterior(bf.signed, iterations = 1e+06) : Index argument required for posterior with multiple numerators.

I don't know why this happens, because the two bf objects (bf, bf.signed) look identical to me. Does anyone know how the get the median d in a one-sided test?

Moritz

• Hi Moritz,

I would apply the two-sided test and then toss out all the negative values for d.

Cheers,
E.J.

• Hi EJ,
thanks, I tried that out. I used

### median d for one-sided test

median(chains[,4][chains[,4]>0])

for that. However, in some cases a really unrealistic high value for d is estimated. I attached an example here https://syncandshare.lrz.de/dl/fiBV1uWpk5kvu2xkKdZDUS1o/onesidedBF.rar

The descriptives are
Low Mean 3.17 SD 0.54
Hig hMean 3.19 SD 0.35
which gives a conventional d of d = 0.03

Without the negative values, d = 0.17 is estimated, in JASP the value is even d = 0.195

In other cases, the one sided d is closer to the two sided value. I really do not know what to make out of that.

• Sure but this makes sense, right? If you look at the mode, it should be near zero. But the median is the 50% cut-off point, so creating a one-sided test makes a big difference. So it is not unrealistically high. It is just that with a non-symmetric distribution, you don't want to summarize with a single point. Looking at the entire distribution is better, imo.
E.J.

• Want do you think of reporting the one-sided BF and the "two-sided" normal d? (of course, annotating that)

• Yes, that is exactly my preferred way of reporting the results!
E.J.