Sample-size determination for the Bayesian t test and Welch's test using the approximate adjusted fractional Bayes...

Area of Science:

• Statistics
• Psychological Research Methods
• Bayesian Inference

Background:

• Comparing independent means is fundamental in statistical analysis.
• Hypotheses of interest include null (μ1 = μ2), two-sided alternative (μ1 ≠ μ2), and one-sided alternative (μ1 > μ2).
• Determining adequate sample size is crucial for reliable hypothesis testing.

Purpose of the Study:

• Introduce the R package SSDbain for sample size determination.
• Facilitate the use of approximate adjusted fractional Bayes factors (AAFBF) for hypothesis evaluation.
• Provide tools for psychological researchers to plan experiments with sufficient power.

Main Methods:

• Utilizes the approximate adjusted fractional Bayes factor (AAFBF) method.
• Implements Bayesian t test and Bayesian Welch's test within the R package.
• Calculates sample size to ensure a desired probability of a Bayes factor exceeding a threshold.

Main Results:

• The SSDbain package provides a method for sample size calculation.
• The R package bain supports the AAFBF implementation.
• Tables are provided to aid researchers in sample size determination.

Conclusions:

• The SSDbain R package simplifies sample size calculation for Bayesian hypothesis testing.
• Psychological researchers can use this package and provided tables to ensure adequate experimental power.
• This contributes to more robust and reliable findings in psychological research.