BFe {BayesRep}

Equality of effect size Bayes factor

Description

Computes the equality of effect size Bayes factor

Usage

BFe(to, so, tr, sr, tau, log = FALSE)

Arguments

to

Original effect estimate

so

Standard error of the original effect estimate

tr

Replication effect estimate

sr

Standard error of the replication effect estimate

tau

The heterogeneity standard deviation \tau under the hypothesis of unequal effect sizes H_1

log

Logical indicating whether the natural logarithm of the Bayes factor should be returned. Defaults to FALSE

Details

The equality of effect size Bayes factor is the Bayes factor contrasting the hypothesis of equal original and replication effect sizes H_0: \theta_o = \theta_r to the hypothesis of unequal effect sizes H_1: \theta_o \neq \theta_r. Under the hypothesis of unequal effect sizes H_1 the study specific effect sizes are assumed to be normally distributed around an overall effect size with heterogeneity standard deviation tau.

Value

The equality of effect size Bayes factor \mathrm{BF}_{01}. \mathrm{BF}_{01} > 1 indicates that the data favour the hypothesis of equal effect sizes H_0 (replication success), whereas \mathrm{BF}_{01} < 1 indicates that the data favour the hypothesis of unequal effect sizes H_1 (replication failure).

Author(s)

Samuel Pawel

References

Bayarri, M. and Mayorall, A. (2002). Bayesian Design of "Successful" Replications. The American Statistician, 56(3): 207-214. doi:10.1198/000313002155

Verhagen, J. and Wagenmakers, E. J. (2014). Bayesian tests to quantify the result of a replication attempt. Journal of Experimental Psychology: General, 145:1457-1475. doi:10.1037/a0036731

Examples

## strong evidence for unequal effect sizes
BFe(to = 1, tr = 0.5, so = sqrt(1/100), sr = sqrt(1/100), tau = 0.3)

## some evidence for equal effect sizes
BFe(to = 1, tr = 1, so = sqrt(1/200), sr = sqrt(1/200), tau = 0.3)