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# Posterior Distribution in Raw Units (t-test)

My question has to do with the posterior distribution and reporting the 95% credible interval in the raw score units. I am very novice when it comes to R but I was able to calculate the raw score units in the BayesFactor package (as noted below

``````  Mean      SD Naive SE Time-series SE
``````

mu -1.3101 0.5116 0.005116 0.005683
sig2 3.2151 1.6501 0.016501 0.018547
delta -0.7912 0.3434 0.003434 0.004059
g 4.2972 33.7041 0.337041 0.345778

1. Quantiles for each variable:

`````` 2.5%     25%     50%     75%   97.5%
``````

mu -2.3197 -1.6468 -1.3042 -0.9805 -0.2914
sig2 1.3409 2.1375 2.8195 3.8277 7.4126
delta -1.4782 -1.0202 -0.7813 -0.5559 -0.1496
g 0.1202 0.3878 0.8359 2.0673 23.0160

My question comes when one uses the "informed prior" tab in JASP. I am unaware of how to add in an informed prior (not centered on zero) to a paired t-test in R. Is there a relatively easy way to do this? If not, is it reasonable to take the standardized effect size in JASP and multiply it by the SD of the difference to produce the posterior distribution in raw units?

• Dear jploenneke,

1. "I am unaware of how to add in an informed prior (not centered on zero) to a paired t-test in R." I'll ask Quentin whether he has R code available (based on https://arxiv.org/pdf/1704.02479.pdf). Not sure whether Richard has included this functionality in his BayesFactor package.
2. "is it reasonable to take the standardized effect size in JASP and multiply it by the SD of the difference to produce the posterior distribution in raw units?" In general, when you try to do such things the problem is that you will use a point estimate for something that really comes with a distribution. But perhaps it may work as an approximation. If you want to make actual predictions about raw values then it would be nice to be able to express uncertainty on that scale, I agree.

Cheers,
E.J.

• Dear jploenneke,

With respect to E.J.'s first point: You can find the corresponding R code here.

Cheers,
Quentin

• Thank you both for your help.