bfPPtheta: Bayes factor for testing effect size

Description

This function computes the Bayes factor contrasting \(H_0\colon \theta = 0\) to \(H_1\colon \theta \sim f(\theta | \code{to}, \code{so}, \alpha)\) for the replication data assuming a normal likelihood. The prior of the effect size \(\theta\) under \(H_1\) is the posterior of the effect size obtained from combining a normal likelihood of the original data raised to the power of \(\alpha\) with a flat initial prior with a. Under \(H_1\), the power parameter can either be fixed to some value between 0 and 1, or it can have a beta distribution \(\alpha | H_1 \sim \mbox{Beta}(\code{x}, \code{y})\).

Usage

bfPPtheta(tr, sr, to, so, x = 1, y = 1, alpha = NA, ...)

Value

Bayes factor (BF > 1 indicates evidence for \(H_0\), whereas BF < 1 indicates evidence for \(H_1\))

Arguments

tr: Effect estimate of the replication study.
sr: Standard error of the replication effect estimate.
to: Effect estimate of the original study.
so: Standard error of the replication effect estimate.
x: Number of successes parameter for beta prior of power parameter under \(H_1\). Defaults to 1. Is only taken into account when alpha = NA.
y: Number of failures parameter for beta prior of power parameter under \(H_1\). Defaults to 1. Is only taken into account when alpha = NA.
alpha: Power parameter under \(H_1\). Can be set to a number between 0 and 1. Defaults to NA.
...: Additional arguments passed to stats::integrate.

Author

Samuel Pawel

Examples

Run this code

## uniform prior on power parameter
bfPPtheta(tr = 0.09,  sr = 0.0518, to = 0.205, so = 0.0506)

## power parameter fixed to alpha = 1
bfPPtheta(tr = 0.090, sr = 0.0518, to = 0.205, so = 0.0506, alpha = 1)