R/p_z.R

In stevemisc: Steve's Miscellaneous Functions

#' Convert the p-value you want to the z-value it actually is
#'
#' @description I \emph{loathe} how statistical instruction privileges obtaining
#'  a magical p-value by reference to an area underneath the standard normal curve,
#'  only to botch what the actual z-value is corresponding to the magical p-value.
#'  This simple function converts the p-value you want (typically .05,
#'  thanks to R.A. Fisher) to the z-value it actually is for the kind of
#'  claims we typically make in inferential statistics. If we're going to do
#'  inference the wrong way, let's at least get the z-value right.
#'
#' @details \code{p_z()} takes a p-value of interest and converts it, with precision,
#' to the z-value it actually is. The function takes a vector and returns a vector. The
#' function assumes you're doing something akin to calculating a confidence interval or
#' testing a regression coefficient against a null hypothesis of zero. This means the default
#' output is a two-sided critical z-value. We're taught to use two-sided z-values when we're
#' agnostic about the direction of the effect or statistic of interest, which is, to be frank,
#' hilarious given how most research is typically done.
#'
#' @param x a numeric vector (one or multiple) between 0 or 1
#' @param ts a logical, defaults to TRUE. If TRUE, returns two-sided critical z-value.
#'  If FALSE, the function returns a one-sized critical z-value.
#'
#' @return This function takes a numeric vector, corresponding to the p-value you want, and
#' returns a numeric vector coinciding with the z-value you want under the standard normal
#' distribution. For example, the z-value corresponding with the magic number of .05 (the
#' conventional cutoff for assessing statistical significance) is not 1.96, it's something
#' like 1.959964 (rounding to the default six decimal points).
#'
#' @examples
#'
#' library(stevemisc)
#'
#' p_z(.05)
#' p_z(c(.001, .01, .05, .1))
#' p_z(.05, ts=FALSE)
#' p_z(c(.001, .01, .05, .1), ts=FALSE)

p_z <- function(x, ts = TRUE) {
  if(ts == TRUE) {
  return(qnorm(x/2, lower.tail = FALSE))
} else {
  return(qnorm(x, lower.tail = FALSE))
}
}