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normality test

This is false. You do not need to fit anything to "derive mean and sd."
Perhaps you have not clearly stated what you mean.
And you want to use Bayesian methods?! 

I would strongly recommend that you seek a competent statistician to work
with. To paraphrase Frank Harrell (with appropriate apologies for
misattribution, if necessary), correspondence courses in brain surgery are
not a good idea.



-- Bert Gunter
Genentech Non-Clinical Statistics
South San Francisco, CA
 
"The business of the statistician is to catalyze the scientific learning
process."  - George E. P. Box