Explanation of the Computational Procedure

Input:

• Design prior (population effect size)
• Bayes factor bound
• Probability

Output:

• Sample size

The results displayed in Part 2 of the fixed-N BFDA module are obtained by repeatedly conducting BFDAs for increasing sample sizes. Each BFDA results in a distribution of Bayes factors. Let’s assume that the selected effect size (design prior for the alternative hypothesis) is true in the population. Then we want to find the sample size for which \(\text{BF}_{10}>\text{bound}\) happens with a probability of \(P(\text{BF}_{10} > \text{bound}) > p\). For computational purposes we convert this into \(P(BF_{10} \leq \text{bound}) \leq 1-p\).

The displayed sample size is the smallest sample size for which this statement is true. Since the simulation results underlying the BFDA app only contain sample sizes in fixed-N BFDA up to 500 observations per group, the message “… you will need more than 500 observations per group to obtain a Bayes factor of…”. If you want to find out the exact number of observations, you will need to conduct additional BFDAs using the simulation script for fixed-N BFDAs and the “NforBF” script available on https://osf.io/3f5qd/.