BFF - Bayes Factor Functions
Bayes factors represent the ratio of probabilities
assigned to data by competing scientific hypotheses. However,
one drawback of Bayes factors is their dependence on prior
specifications that define null and alternative hypotheses.
Additionally, there are challenges in their computation. To
address these issues, we define Bayes factor functions (BFFs)
directly from common test statistics. BFFs express Bayes
factors as a function of the prior densities used to define the
alternative hypotheses. These prior densities are centered on
standardized effects, which serve as indices for the BFF.
Therefore, BFFs offer a summary of evidence in favor of
alternative hypotheses that correspond to a range of
scientifically interesting effect sizes. Such summaries remove
the need for arbitrary thresholds to determine "statistical
significance." BFFs are available in closed form and can be
easily computed from z, t, chi-squared, and F statistics. They
depend on hyperparameters "r" and "tau^2", which determine the
shape and scale of the prior distributions defining the
alternative hypotheses. Plots of BFFs versus effect size
provide informative summaries of hypothesis tests that can be
easily aggregated across studies.
