Bayesian estimation for two groups provides complete distributions of credible values for the effect size, group means and their difference, standard deviations and their difference, and the normality of the data. The method handles outliers. The decision rule can accept the null value (unlike traditional t tests) when certainty in the estimate is high (unlike Bayesian model com- parison using Bayes factors). The method also yields precise estimates of statistical power for various research goals. The software and programs are free, and run on Macintosh, Windows, and Linux platforms. Bayesian estimation supersedes the t test