bfpwr (version 0.1.6)

nbf01: Sample size determination for z-test Bayes factor

Description

This function computes the required sample size to obtain a Bayes factor (bf01) more extreme than a threshold k with a specified target power.

Usage

nbf01(
  k,
  power,
  usd,
  null = 0,
  pm,
  psd,
  dpm = pm,
  dpsd = psd,
  nrange = c(1, 10^5),
  lower.tail = TRUE,
  integer = TRUE,
  analytical = TRUE,
  ...
)

Value

The required sample size to achieve the specified power

Arguments

k

Bayes factor threshold

power

Target power

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

pm

Mean of the normal prior assigned to the parameter under the alternative in the analysis

psd

Standard deviation of the normal prior assigned to the parameter under the alternative in the analysis. Set to 0 to obtain a point prior at the prior mean

dpm

Mean of the normal design prior assigned to the parameter. Defaults to the same value as the analysis prior pm

dpsd

Standard deviation of the normal design prior assigned to the parameter. Defaults to the same value as the analysis prior psd

nrange

Sample size search range over which numerical search is performed. Defaults to c(1, 10^5)

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

integer

Logical indicating whether only integer valued sample sizes should be returned. If TRUE the required sample size is rounded to the next larger integer. Defaults to TRUE

analytical

Logical indicating whether analytical (if available) or numerical method should be used. Defaults to TRUE

...

Other arguments passed to stats::uniroot

Author

Samuel Pawel

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.

See Also

pbf01, powerbf01, bf01

Examples

## point alternative (analytical and numerical solution available)
nbf01(k = 1/10, power = 0.9, usd = 1, null = 0, pm = 0.5, psd = 0,
      analytical = c(TRUE, FALSE), integer = FALSE)

## standardized mean difference (usd = sqrt(2), effective sample size = per group size)
nbf01(k = 1/10, power = 0.9, usd = sqrt(2), null = 0, pm = 0, psd = 1)
## this is the sample size per group (assuming equally sized groups)

## z-transformed correlation (usd = 1, effective sample size = n - 3)
nbf01(k = 1/10, power = 0.9, usd = 1, null = 0, pm = 0.2, psd = 0.5)
## have to add 3 to obtain the actual sample size

## log hazard/odds ratio (usd = 2, effective sample size = total number of events)
nbf01(k = 1/10, power = 0.9, usd = 2, null = 0, pm = 0, psd = sqrt(0.5))
## have to convert the number of events to a sample size