ptbf01: Cumulative distribution function of the t-test Bayes factor

Description

This function computes the probability of obtaining a \(t\)-test Bayes factor (tbf01) more extreme than a threshold k with a specified sample size.

Usage

ptbf01(
  k,
  n,
  n1 = n,
  n2 = n,
  null = 0,
  plocation = 0,
  pscale = 1/sqrt(2),
  pdf = 1,
  dpm = plocation,
  dpsd = pscale,
  type = c("two.sample", "one.sample", "paired"),
  alternative = c("two.sided", "less", "greater"),
  lower.tail = TRUE,
  drange = "adaptive",
  ...
)

Value

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

Arguments

k: Bayes factor threshold
n: Sample size (per group)
n1: Sample size in group 1 (only required for two-sample \(t\)-test with unequal group sizes)
n2: Sample size in group 2 (only required for two-sample \(t\)-test with unequal group sizes)
null: Standardized mean difference under the point null hypothesis. Defaults to 0
plocation: \(t\) prior location. Defaults to 0
pscale: \(t\) prior scale. Defaults to 1/sqrt(2)
pdf: \(t\) prior degrees of freedom. Defaults to 1 (a Cauchy prior)
dpm: Mean of the normal design prior assigned to the standardized mean difference. Defaults to the analysis prior location
dpsd: Standard deviation of the normal design prior assigned to the standardized mean difference. Set to 0 to obtain a point prior at the design prior mean. Defaults to the analysis prior scale
type: Type of \(t\)-test. Can be "two.sample" (default), "one.sample", or "paired"
alternative: Direction of the test. Can be either "two.sided" (default), "less", or "greater". The latter two truncate the analysis prior to negative and positive effects, respectively. If set to "less" or "greater", the power is only computed based on data with effect estimates in the direction of the alternative
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
drange: Standardized mean difference search range over which the critical values are searched for. Can be either set to a numerical range or to "adaptive" (default) which determines the range in an adaptive way from the other input parameters
...: Other arguments passed to stats::uniroot

Author

Samuel Pawel

Examples

Run this code

## example from Schönbrodt and Wagenmakers (2018, p. 135)
ptbf01(k = 1/6, n = 146, dpm = 0.5, dpsd = 0, alternative = "greater")
ptbf01(k = 6, n = 146, dpm = 0, dpsd = 0, alternative = "greater",
       lower.tail = FALSE)

## two-sided
ptbf01(k = 1/6, n = 146, dpm = 0.5, dpsd = 0)
ptbf01(k = 6, n = 146, dpm = 0, dpsd = 0, lower.tail = FALSE)

## one-sample test
ptbf01(k = 1/6, n = 146, dpm = 0.5, dpsd = 0, alternative = "greater", type = "one.sample")