bft: Bayes factor from t-statistic

In nisone: Inference for Samples of Size at Least One

Bayes factor from t-statistic

Description

Given a user-provided prior on the standardized effect size, will calculate the Bayes factor.

Usage

bft(t, nu, nd, prior = NULL)

Arguments

t	The observed t-statistic.
nu	The degrees of freedom of the t-statistic. This should be n-1 in the one-sample case. This should be n_1+n_2-2 in the two-sample case.
nd	Effective sample size. This should be n in the one-sample case. This should be (\frac{1}{n_1} + \frac{1}{n_2})^{-1} in the two-sample case.
prior	The prior on the standardized effect size, \delta. In the one-sample case this is the prior over \delta = \frac{\mu - \mu_0}{\sigma}, where \mu_0 is the null value. In the two-sample case this is the prior over \delta = \frac{\mu_1 - \mu_2}{\sigma}, where \mu_1 and \mu_2 are the means of the two-samples. The default prior is a Cauchy, but you can put in any density function you want. If your prior has pointmasses in it, this function won't work.

Details

Let \delta be the standardized effect size, let \sigma^2 be the variance (assumed equal in two-sample case). In the one-sample case, \delta = \frac{\mu - \mu_0}{\sigma}, where \mu_0 is the null value. In the two-sample case, \delta = \frac{\mu_1 - \mu_2}{\sigma}, where \mu_1 and \mu_2 are the means of the two-samples. We place the prior 1/\sigma^2 under the null and \pi(\delta)/\sigma^2 under the alternative, for some arbitrary density \pi(\cdot). Given this setting, the Bayes factor is a function of the t-statistic. We calculate it via numeric integration.

Value

The Bayes factor to a corresponding t-statistic.

Author(s)

David Gerard

References

• Gronau, Q. F., Ly, A., & Wagenmakers, E. J. (2020). Informed Bayesian t-tests. The American Statistician. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/00031305.2018.1562983")}

Examples

# One sample t, n = 10, t-statistic = 2
bft(t = 2, nu = 10 - 1, nd = 10)

# Two sample t, n1 = 10, n2 = 8, t-statistic = 2
bft(t = 2, nu = 10 + 8 - 2, nd = 1 / (1 / 10 + 1 / 8))

nisone documentation built on Sept. 8, 2026, 5:08 p.m.