Bayesian estimation supersedes the t test.

TLDR

Bayesian estimation for two groups yields full posterior distributions of effect sizes, group means, their differences, standard deviations, and normality assessments. The method handles outliers, permits accepting the null when certainty is high, and is freely available on Macintosh, Windows, and Linux. It provides precise estimates of statistical power for a range of research objectives.

Abstract

Bayesian estimation for 2 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 comparison 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.