Equivalence Test for Two Means by TOST (Two One-Sided Test) Procedure

mean.equiv.tost.test <- function(x, y, margin=1, alpha=0.05) {
  ## Equivalence Test for Two Means by TOST (Two One-Sided Test) Procedure
  ## Assumption: Normality. 
  ## Reference: Understanding Equivalence and Noninferiority Testing (Walker and Nowacki)
  ## INPUT:
  ##    x: a vector of continuous scale.
  ##    y: another vector of continuous scale (to compare with x)
  ##    margin: Equivalence Margin (defaul to 1)
  ##    alpha: Significance Level.
  cl <- 1 - 2 * alpha
  a <- t.test(x, y, conf.level=cl)
  ci <- a$conf.int

  print(a)

  cat("Equivalence Test for Two Means by TOST Procedure:\n")
  cat("Equivalence Margin =", margin, "\n")

  if (ci[1] >= -margin && ci[2] <= margin) {
    cat("Equivalence Established! (Significance Level =", 100*alpha, "%)\n\n")
  } else cat("Equivalence NOT Established. (Significance Level =", 100*alpha, "%)\n\n")

  plot(0, 0, xlim=c(-2*margin, 2*margin), ylim=c(-1,1), axes=F, xlab="Difference in Efficacies", ylab="", type="n")
  axis(side=1, at=c(-2*margin, -margin, 0, margin, 2*margin), labels=c("", paste("-", margin), "0", margin, ""))
  abline(v=c(-margin, 0, margin), lty=c(2,1,2))
  lines(ci, c(0,0), lwd=3)
  lines(rep(ci[1], 2), c(-0.1, 0.1), lwd=2)
  lines(rep(ci[2], 2), c(-0.1, 0.1), lwd=2)
  lines(rep(-diff(a$estimate), 2), c(-0.1, 0.1), lwd=4)
}
if (F) {
  mean.equiv.tost.test(rnorm(20), rnorm(20, mean=0.3))
}