The minimum Bayes factor hypothesis test for correlations and partial correlations. Issue 11 (3rd June 2021) - Chen, Fang; Ye, Keying; Wang, Min
Abstract: In this paper, we follow the work [Held, L., and M. Ott. 2016. How the maximal evidence of p-values against point null hypotheses depends on sample size. The American Statistician 70 (4):335–41] and propose a sample-size adjusted minimum Bayes factor (minBF) for testing the presence of a correlation or a partial correlation. The proposed minBF is related to the two-sided p -value from the frequentist test and can be easily calculated using either a pocket calculator or spreadsheets, so long as the researcher is familiar with the frequentist paradigm. It turns out that the minBF increases with an increasing sample size, which implies that the maximal evidence of the two-sided p -value decreases with an increasing sample size. Simulation studies and two real-data applications are provided for illustrative purposes.