Package {alphaN}

Title:	Set Alpha Based on Sample Size Using Bayes Factors
Version:	0.2.0
Description:	Sets the alpha level for coefficients in a regression model as a decreasing function of the sample size through the use of Jeffreys' Approximate Bayes factor. You tell alphaN() your sample size, and it tells you to which value you must lower alpha to avoid Lindley's Paradox. For details, see Wulff and Taylor (2024) <doi:10.1177/14761270231214429>. Alpha can also be calibrated to the effect-size and moment Bayes factors of Klauer, Meyer-Grant, and Kellen (2024) <doi:10.3758/s13423-024-02612-2>, which center the alternative hypothesis on an effect size of your choosing.
License:	MIT + file LICENSE
URL:	https://github.com/jespernwulff/alphaN, https://jespernwulff.github.io/alphaN/
BugReports:	https://github.com/jespernwulff/alphaN/issues
Depends:	R (≥ 4.0)
Suggests:	knitr, rmarkdown, spelling, testthat (≥ 3.0.0)
VignetteBuilder:	knitr
Config/testthat/edition:	3
Encoding:	UTF-8
Language:	en-US
RoxygenNote:	7.3.3
NeedsCompilation:	no
Packaged:	2026-07-11 20:52:38 UTC; au205643
Author:	Jesper Wulff [aut, cre], Luke Taylor [aut]
Maintainer:	Jesper Wulff <jwulff@econ.au.dk>
Repository:	CRAN
Date/Publication:	2026-07-12 08:40:14 UTC

Transforms a t-statistic from a glm or lm object into Jeffreys' approximate Bayes factor

Description

Extracts the test statistic of a coefficient from a fitted model object and converts it into Jeffreys' approximate Bayes factor, given the sample size used in the fit.

Usage

JAB(glm_obj, covariate, method = "JAB", upper = 1)

Arguments

Value

A numeric value for the BF in favour of H1.

Examples

# Simulate data

## Sample size
n <- 200

## Regressors
Z1 <- runif(n, -1, 1)
Z2 <- runif(n, -1, 1)
Z3 <- runif(n, -1, 1)
Z4 <- runif(n, -1, 1)
X <- runif(n, -1, 1)

## Error term
U <- rnorm(n, 0, 0.5)

## Outcome
Y <- X/sqrt(n) + U

# Run a GLM
LM <- glm(Y ~ X + Z1 + Z2 + Z3 + Z4)

# Compute JAB for "X" based on the regression results
JAB(LM, "X")

# Compute JAB using the minimum prior
JAB(LM, "X", method = "min")

Plots JAB as a function of the p-value

Description

Plots JAB as a function of the p-value

Usage

JAB_plot(n, BF = 1, method = "JAB", upper = 1)

Arguments

Value

Prints a plot.

Examples

# Plot JAB as function of the p-value for a sample size of 2000
JAB_plot(2000)

Transforms a p-value into Jeffreys' approximate Bayes factor

Description

Converts a two-sided p-value from a z- or t-test into Jeffreys' approximate Bayes factor, given the sample size.

Usage

JABp(n, p, z = TRUE, df = NULL, method = "JAB", upper = 1)

Arguments

Value

A numeric value for the BF in favour of H1.

Examples

# Transform a p-value of 0.007038863 from a z-test into JAB
# using a sample size of 200.
JABp(200, 0.007038863)

# Transform a p-value of 0.007038863 from a t-test with 190
# degrees of freedom into JAB using a sample size of 200.
JABp(200, 0.007038863, z=FALSE, df=190)

Transforms a t-statistic into Jeffreys' approximate Bayes factor

Description

Converts a t-statistic (or z-statistic) into Jeffreys' approximate Bayes factor, given the sample size. Vectorized over n and t.

Usage

JABt(n, t, method = "JAB", upper = 1)

Arguments

Value

A numeric value for the BF in favour of H1.

Examples

# Transform a t-statistic of 2.695 computed based on a sample size of 200 into JAB
JABt(200, 2.695)

Set the alpha level based on sample size for coefficients in a regression model

Description

Computes the alpha level required to achieve a desired level of evidence, expressed as a Bayes factor, when testing a coefficient in a regression model. The alpha level is a decreasing function of the sample size. Vectorized over n and BF.

Usage

alphaN(n, BF = 1, method = "JAB", upper = 1, de = 0.5, nu = NULL, r = NULL)

Arguments

Details

For methods "ES" and "moment", the alpha level is found by solving for the critical t value at which the effect-size or moment Bayes factor equals BF, and converting that critical value to a two-sided p-value on the t distribution with n - 1 degrees of freedom (the one-sample / single-coefficient case of Klauer et al., 2024). The implementation is validated against the Bayes factors reported in Table 7 of that paper. Because the moment prior assigns effects near zero a priori density zero, the alpha level it implies decreases much faster with n than under JAB.

As a special case, setting method = "ES", nu = 1, de = 0 with an explicit scale (e.g. r = 1) calibrates alpha to the default (Jeffreys-Zellner-Siow type) Bayes factor of Rouder et al. (2009).

For n greater than 50,000, methods "ES" and "moment" evaluate the noncentral-t density ratio in its normal limit, which is accurate to a fraction of a percent there.

Value

Numeric alpha level required to achieve the desired level of evidence.

References

Gu et al. (2016). Error probabilities in default Bayesian hypothesis testing. Journal of Mathematical Psychology, 72, 130–143.

Gu et al. (2018). Approximated adjusted fractional Bayes factors: A general method for testing informative hypotheses. The British Journal of Mathematical and Statistical Psychology, 71(2).

Klauer, K. C., Meyer-Grant, C. G., & Kellen, D. (2024). On Bayes factors for hypothesis tests. Psychonomic Bulletin & Review. doi:10.3758/s13423-024-02612-2

O’Hagan, A. (1995). Fractional Bayes Factors for Model Comparison. Journal of the Royal Statistical Society. Series B (Methodological), 57(1), 99–138.

Rouder, J. N., Speckman, P. L., Sun, D., Morey, R. D., & Iverson, G. (2009). Bayesian t tests for accepting and rejecting the null hypothesis. Psychonomic Bulletin & Review, 16, 225–237.

Wagenmakers, E.-J. (2022). Approximate objective Bayes factors from p-values and sample size: The 3p(sqrt(n)) rule. PsyArXiv.

Wulff, J. N., & Taylor, L. (2024). How and why alpha should depend on sample size: A Bayesian-frequentist compromise for significance testing. Strategic Organization. doi:10.1177/14761270231214429

Examples

# Plot of alpha level as a function of n
seqN <- seq(50, 1000, 1)
plot(seqN, alphaN(seqN), type = "l")

# Alpha calibrated to the effect-size Bayes factor (Klauer et al., 2024),
# targeting moderate evidence for a medium-sized effect
alphaN(1000, BF = 3, method = "ES", de = 0.5)

# The same calibration under the moment Bayes factor
alphaN(1000, BF = 3, method = "moment", de = 0.5)

Creates a plot of alpha as function of sample size for each of the four prior options

Description

Creates a plot of alpha as function of sample size for each of the four prior options

Usage

alphaN_plot(BF = 1, max = 10000, ylim = NULL)

Arguments

Value

Prints a plot.

Examples

# Plot of alpha level as a function of n for a Bayes factor of 3
alphaN_plot(BF = 3)