The posterior distribution, showing complete distributions of the difference of means (right middle), the difference of standard deviations, the effect size (right bottom), and posterior predictive check (right upper).

Bayesian estimation supersedes the t test.

John K. Kruschke, Journal of Experimental Psychology: General

Abstract:

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 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, Linux, and Windows platforms.

The article:

Get the article here^* or at doi: 10.1037/a0029146.
^*Your click on this link constitutes your request to me for a personal copy of the linked article, and my delivery of a personal copy. Any other use is prohibited.

Videos:

Watch the video, and this additional video that includes discussion of sequential testing. (Both presented at the 2012 Psychonomic Society meeting.)

And here is a video about how to install the software and run it.

Software (named "BEST" for "Bayesian estimation"):

There is (as of January 3, 2013) a web app created by Rasmus Bååth that provides the primary results of BEST without any need to install software. Just paste in your data and click a button. See the blog post.

Get the BEST programs from this zip file. Updated January 23, 2013. Be sure to unzip (extract) the zip file after it is saved on you computer. For information about running the programs, see the comments at the top of the file BESTexample.R.

The programs now (as of Sept. 3, 2012) include a version for estimating the parameters of a single group. The 1-group version is named BEST1G.R. See the example in BEST1Gexample.R and this blog post.

For information about installing the software (R, JAGS, rjags, and RStudio), see the comments at the top of the file BESTexample.R, or at this blog post.

A video about software installation and running an example is here.

Learn more:

For a complete tutorial about Bayesian methods, see the book.

You can make comments at the blog. Search the blog with the phrase "Bayesian estimation".