[An updated post appears HERE.]
It's been said that if all you're doing is a t test, Bayesian methods don't get you anything more. Wrong! Here's a manuscript showing that robust Bayesian estimation (not Bayesian model comparison involving Bayes factors) produces far more information about the difference of means, the difference of standard deviations, the influence of outliers, and power of the test. The Bayesian method can also accept the null, not merely reject it. The software and programs are free and easy to use. It is time for robust Bayesian estimation to supersede traditional methods.