R/ztest.1samp.R

In powertools: Power and Sample Size Tools

#' Power calculation for one-sample z test
#'
#' @description
#' This function performs power and sample size calculations for a one-sample z test
#' which is analogous to a one-sample t test with the variance assumed to be known.
#' This function is provided largely for pedagogical purposes; in general,
#' for real studies, the one-sample t test procedure should be used.
#'
#' @param N The sample size.
#' @param delta muA (the true mean) - mu0 (the mean under the null).
#' @param sd The standard deviation; defaults to 1.
#' @param alpha The significance level (type 1 error rate); defaults to 0.05.
#' @param power The specified level of power.
#' @param sides Either 1 or 2 (default) to specify a one- or two- sided hypothesis test.
#' @param v Either TRUE for verbose output or FALSE (default) to output computed argument only.
#'
#' @return A list of the arguments (including the computed one).
#' @export
#'
#' @examples
#' ztest.1samp(N = NULL, delta = 6.5 - 5.7, sd = 2, power = 0.8, sides = 2)
#' ztest.1samp(N = 40, delta = NULL, sd = 1, power = 0.9, sides = 2)
#' ztest.1samp(N = NULL, delta = 0.6, sd = 1, power = 0.8, sides = 1)

ztest.1samp <- function (N = NULL, delta = NULL, sd = 1,
                         alpha = 0.05, power = NULL, sides = 2,
                         v = FALSE) {

  # Check if the arguments are specified correctly
  check.many(list(N, delta, sd, alpha, power), "oneof")
  check.param(N, "pos")
  check.param(delta, "num")
  check.param(sd, "pos")
  check.param(alpha, "unit")
  check.param(power, "unit")
  check.param(sides, "req"); check.param(sides, "vals", valslist = c(1, 2))
  check.param(v, "req"); check.param(v, "bool")

  # Calculate power
  if (sides == 1)
    p.body <- quote({
      d <- abs(delta) / sd
      stats::pnorm(stats::qnorm(alpha) + sqrt(N) * d)
    })
  else if (sides == 2)
    p.body <- quote({
      d <- delta / sd
      stats::pnorm(stats::qnorm(alpha / 2) + sqrt(N) * d) +
      stats::pnorm(stats::qnorm(alpha / 2) - sqrt(N) * d)
    })

  # Use stats::uniroot function to calculate missing argument
  if (is.null(power)) {
    power <- eval(p.body)
    if (!v) return(power)
  }
  else if (is.null(N)) {
    N <- stats::uniroot(function(N) eval(p.body) - power, c(2, 1e+07))$root
    if (!v) return(N)
  }
  else if (is.null(sd)) {
    sd <- stats::uniroot(function(sd) eval(p.body) - power, delta * c(1e-07, 1e+07))$root
    if (!v) return(sd)
  }
  else if (is.null(delta)) {
    delta <- stats::uniroot(function(delta) eval(p.body) - power,  c(1e-07, 1e+07))$root
    if (!v) return(delta)
  }
  else if (is.null(alpha)) {
    alpha <- stats::uniroot(function(alpha) eval(p.body) - power, c(1e-10, 1 - 1e-10))$root
    if (!v) return(alpha)
  }
  else stop("internal error")

  # Generate output text
  METHOD <- "One-sample z test power calculation"

  # Print output as a power.htest object
  structure(list(N = N, delta = delta, sd = sd, alpha = alpha,
                 power = power, sides = sides,
                 method = METHOD), class = "power.htest")
}