R/data-penetrating_oil.R

In openintro: Data Sets and Supplemental Functions from 'OpenIntro' Textbooks and Labs

#' What's the best way to loosen a rusty bolt?
#'
#' The channel Project Farm on YouTube investigated penetrating oils and other
#' options for loosening rusty bolts. Eight options were evaluated, including a
#' control group, to determine which was most effective.
#'
#'
#' @name penetrating_oil
#' @docType data
#' @format A data frame with 30 observations on the following 2 variables.
#' \describe{
#'   \item{treatment}{The different treatments tried:
#' \code{none} (control), \code{Heat} (via blow torch), \code{Acetone/ATF},
#' \code{AeroKroil}, \code{Liquid Wrench}, \code{PB Blaster}, \code{Royal
#' Purple}, and \code{WD-40}.}
#'   \item{torque}{Torque required to loosen the rusty bolt,
#' which was measured in foot-pounds.}
#' }
#' @source \url{https://www.youtube.com/watch?v=xUEob2oAKVs}
#' @keywords datasets
#' @examples
#'
#' m <- lm(torque ~ treatment, data = penetrating_oil)
#' anova(m)
#'
#' # There are 28 pairwise comparisons to be made.
#' xbar <- tapply(penetrating_oil$torque, penetrating_oil$treatment, mean)
#' n <- tapply(penetrating_oil$torque, penetrating_oil$treatment, length)
#' s <- summary(m)$sigma
#' df <- summary(m)$df[1]
#'
#' diff <- c()
#' se <- c()
#' k <- 0
#' N <- length(n)
#' K <- N * (N - 1) / 2
#' for (i in 1:(N - 1)) {
#'   for (j in (i + 1):N) {
#'     k <- k + 1
#'     diff[k] <- xbar[i] - xbar[j]
#'     se[k] <- s * sqrt(1 / n[i] + 1 / n[j])
#'     if (2 * K * pt(-abs(diff[k] / se[k]), df) < 0.05) {
#'       cat("0.05 - ", names(n)[c(i, j)], "\n")
#'     } else if (2 * K * pt(-abs(diff[k] / se[k]), df) < 0.1) {
#'       cat("0.1 - ", names(n)[c(i, j)], "\n")
#'     } else if (2 * K * pt(-abs(diff[k] / se[k]), df) < 0.2) {
#'       cat("0.2 - ", names(n)[c(i, j)], "\n")
#'     } else if (2 * K * pt(-abs(diff[k] / se[k]), df) < 0.3) {
#'       cat("0.3 - ", names(n)[c(i, j)], "\n")
#'     }
#'   }
#' }
#'
#' # Smallest p-value using Bonferroni
#' min(2 * K * pt(-abs(diff / se), df))
#'
#'
#' # Better pairwise comparison method.
#' anova(m1 <- aov(torque ~ treatment, data = penetrating_oil))
#' TukeyHSD(m1)
"penetrating_oil"