R/LR_test_2x2.R

In contingencytables: Statistical Analysis of Contingency Tables

#' @title The likelihood ratio test for association in 2x2 tables
#' @description The likelihood ratio test for association in 2x2 tables
#' @description Described in Chapter 4 "The 2x2 Table"
#' @param n the observed counts (a 2x2 matrix)
#' @examples
#' LR_test_2x2(tea)
#' LR_test_2x2(perondi_2004)
#' LR_test_2x2(lampasona_2013)
#' LR_test_2x2(ritland_2007)
#' @export
#' @return An object of the [contingencytables_result] class,
#' basically a subclass of [base::list()]. Use the [utils::str()] function
#' to see the specific elements returned.
LR_test_2x2 <- function(n) {
  validateArguments(mget(ls()))

  # The estimated expected counts
  N <- sum(n)
  m <- outer(apply(n, 1, sum), apply(n, 2, sum)) / N

  # The likelihood ratio statistic
  T0 <- 0
  for (i in 1:2) {
    for (j in 1:2) {
      if (n[i, j] > 0) {
        T0 <- T0 + n[i, j] * log(n[i, j] / m[i, j])
      }
    }
  }
  T0 <- 2 * T0

  # The two-sided P-value (reference distribution: chi-squared with 1 degree of freedom)
  df <- 1
  P <- 1 - pchisq(T0, df)

  return(
    contingencytables_result(
      list("Pvalue" = P, "T" = T0, "df" = df),
      sprintf("The likelihood ratio test: P = %7.5f, T = %5.3f (df = %i)", P, T0, df)
    )
  )
}