  Bayes factors are an increasingly popular tool for indexing evidence from
experiments. For two competing population models, the Bayes factor reflects the
relative likelihood of observing some data under one model compared to the
other. In general, computing a Bayes factor is difficult, because computing the
marginal likelihood of each model requires integrating the product of the
likelihood and a prior distribution on the population parameter(s). In this
paper, we develop a new analytic formula for computing Bayes factors directly
from minimal summary statistics in repeated-measures designs. This work is an
improvement on previous methods for computing Bayes factors from summary
statistics (e.g., the BIC method), which produce Bayes factors that violate the
Sellke upper bound of evidence for smaller sample sizes. The new approach taken
in this paper extends requires knowing only the $F$-statistic and degrees of
freedom, both of which are commonly reported in most empirical work. In
addition to providing computational examples, we report a simulation study that
benchmarks the new formula against other methods for computing Bayes factors in
repeated-measures designs. Our new method provides an easy way for researchers
to compute Bayes factors directly from a minimal set of summary statistics,
allowing users to index the evidential value of their own data, as well as data
reported in published studies.
