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# How does sample size "work" for Bayesian statistics?

Hello everyone,
I've just started reading into Bayesian statistics and I'm pretty smitten by it even though I haven't fully understood all of it yet.
I'm a PhD student and I'm considering using Bayesian statistics for my sample. I'm looking at humans in Isolated and Confined Environments (ICE), which means that by default the data is extremely difficult to obtain and the sample size is tiny. The issue is that the total possible population is exactly 11 people, of whom 1 has withdrawn from the study and 1 may need to be excluded from the data. The person who may need to be excluded has developed major psychiatric problems and has been evacuated. Even though I will be able to collect more data from them, this will be from their home country/town and not from within the ICE, so it makes no sense to include that data in the the ICE analysis.
I do have an age & gender-matched control group.

So, would Bayesian statistics even be appropriate? I've found a paper (Stiger et al., 1998) that suggests you can use normal ANOVA with small samples and ordinal data if you use a Huyn-Feldt correction, but I can't seem to find a direct answer for Bayesian statistics...

eniseg the newbie

• Hi Eniseg the newbie, :-)

Bayesian statistics does not require small-sample corrections. With small samples, there is likely to be little information in the data, which means that the prior distributions will not change a lot. So you are likely not to learn a lot from a small sample, but you might get lucky (i.e., the effect might be overwhelming). Essentially, the Bayesian framework operates with few samples, many samples, and even no samples at all :-)

Cheers,
E.J.

• Hi EJ

Thank you so much! That was so helpful. Currently my Bayes Factors come out between 1-4, so that's supposed to be between anecdotal evidence and moderate evidence. Both of these suit in well with the theoretical background.

Thank you so much!!
eniseg

• Would you have any references that refer to the sample size for the Bayesian Paired Samples T-Test and more generally for Bayesian statistics ?