Bayes factor functions

Interpreting the evidence provided by experimental and observational studies is essential to the process of scientific discovery. The most commonly used indirect measures of evidence are P-values. Unfortunately, P-values do not directly reflect the probability that a new discovery has been made and are often mis-interpreted. Bayes factors represent an informative alternative to P-values for reporting outcomes of hypothesis tests. They provide direct measures of the relative support that data provide to competing hypotheses and are able to quantify support for true null hypotheses. The Bayes factor functions developed in this project will be defined from classical test statistics and will summarize evidence in support of scientific discoveries. The resulting Bayes factor functions will provide clear summaries of the outcome from a single experiment, eliminate arbitrary P-value thresholds, and are ideal for combining evidence from replicated studies. They will enhance both the reproducibility and replicability of scientific studies. The project will also provide research training for graduate students. The Bayes factor functions developed in this project will advance Bayesian testing theory and application in several ways. These include defining Bayes factors directly from classical test statistics (which are readily available from standard statistical analyses); modeling the distributions of these test statistics as functions of standardized effect sizes (the quantities of primary interest in scientific and observational studies); specifying scientific hypotheses so that there is a clear distinction between the null hypothesis of no scientific/treatment effect versus a new effect or benefit; and providing easily calculable expressions for the Bayes factors corresponding to given effect sizes. These innovations will allow scientists to easily assess statistical evidence arising from scientific studies conducted across a wide range of scientific disciplines. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.