pnmbf01: Cumulative distribution function of the normal moment prior...

In bfpwr: Power and Sample Size Calculations for Bayes Factor Analysis

Cumulative distribution function of the normal moment prior Bayes factor

Description

This function computes the probability of obtaining a normal moment prior Bayes factor (nmbf01) more extreme than a threshold k with a specified sample size.

Usage

pnmbf01(k, n, usd, null = 0, psd, dpm, dpsd, lower.tail = TRUE)

Arguments

k	Bayes factor threshold
n	Sample size
usd	Unit standard deviation, the (approximate) standard error of the parameter estimate based on \code{n}=1, see details
null	Parameter value under the point null hypothesis. Defaults to 0
psd	Spread of the normal moment prior assigned to the parameter under the alternative in the analysis. The modes of the prior are located at \pm\sqrt{2}\,\code{psd}
dpm	Mean of the normal design prior assigned to the parameter
dpsd	Standard deviation of the normal design prior assigned to the parameter. Set to 0 to obtain a point prior at the design prior mean
lower.tail	Logical indicating whether Pr(\mathrm{BF}_{01} \leq k) (TRUE) or Pr(\mathrm{BF}_{01} > k) (FALSE) should be computed. Defaults to TRUE

Details

It is assumed that the standard error of the future parameter estimate is of the form \code{se} =\code{usd}/\sqrt{\code{n}}. For example, for normally distributed data with known standard deviation sd and two equally sized groups of size n, the standard error of an estimated standardized mean difference is \code{se} = \code{sd}\sqrt{2/n}, so the corresponding unit standard deviation is \code{usd} = \code{sd}\sqrt{2}. See the vignette for more information.

Value

The probability that the Bayes factor is less or greater (depending on the specified lower.tail) than the specified threshold k

Author(s)

Samuel Pawel

See Also

nmbf01, nnmbf01, powernmbf01

Examples

## point desing prior (psd = 0)
pnmbf01(k = 1/10, n = 200, usd = 2, null = 0, psd = 0.5/sqrt(2), dpm = 0.5, dpsd = 0)

## normal design prior to incorporate parameter uncertainty (psd > 0)
pnmbf01(k = 1/10, n = 200, usd = 2, null = 0, psd = 0.5/sqrt(2), dpm = 0.5, dpsd = 0.25)

## design prior is the null hypothesis (dpm = 0, dpsd = 0)
pnmbf01(k = 10, n = 200, usd = 2, null = 0, psd = 0.5/sqrt(2), dpm = 0, dpsd = 0,
        lower.tail = FALSE)

bfpwr documentation built on June 8, 2025, 1:40 p.m.