The journal Basic and Applied Social Psychology has stated a "ban" on p-values. The specific rules for publication are: p-values and classic null hypothesis significance testing (NHST) procedures are deemed to be inadequate and are to be replaced with rigorous descriptive statistics and effect sizes.
Kevin Boone has a great introduction to Bayesian statistics with some very simple examples to begin to comprehend how Bayesian statistics are calculated. But, as he notes, it is only scratching the surface of how to apply Bayesian stats. Currently, people report Bayesian statistics in
Why would you want to use Bayesian statistics? Some basics about Bayesian stats vs traditional stats
rtxi89 left a comment on my last post asking to have a full explanation for Bayesian statistics. It's true, many people have heard about Bayesian statistics, but it's not commonly known about -- and definitely not common in the field of psychology as of present. Now,
Bayesian statistics are interesting as they give credence to the idea that stats can be interpretable and statistically meaningful without having to do post-hoc corrections and analyses. Two papers (and one review), one from Masson (2011) and one from Wagenmakers (2007) (with a nice review of