Bayes factor functions for reporting outcomes of hypothesis tests.

Area of Science:

• Statistical inference
• Hypothesis testing

Background:

• P-values are widely used but have limitations in hypothesis testing.
• Bayes factors offer a direct measure of evidence for competing hypotheses.
• Calculating Bayes factors can be challenging, especially in high-dimensional settings.

Purpose of the Study:

• To introduce Bayes factor functions (BFFs) as a practical alternative to P-values.
• To simplify Bayes factor computation and interpretation in hypothesis testing.
• To provide informative summaries of hypothesis tests that can be aggregated across studies.

Main Methods:

• Defined BFFs directly from common test statistics (z, t, χ², F).
• Expressed BFFs as a function of a single noncentrality parameter related to standardized effect sizes.
• Utilized nonlocal alternative prior densities for efficient evidence accumulation.

Main Results:

• BFFs can be computed easily in closed form from standard test statistics.
• Plots of BFFs versus effect size offer informative, aggregable summaries of hypothesis tests.
• BFFs eliminate the need for arbitrary P-value thresholds for statistical significance.

Conclusions:

• BFFs provide a robust and interpretable alternative to P-values for hypothesis testing.
• BFFs facilitate the aggregation of evidence across studies, moving beyond significance thresholds.
• The proposed method simplifies Bayes factor computation and enhances statistical reporting.