openintro (version 2.4.0)

penetrating_oil: What's the best way to loosen a rusty bolt?

Description

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.

Usage

penetrating_oil

Format

A data frame with 30 observations on the following 2 variables.

treatment

The different treatments tried: none (control), Heat (via blow torch), Acetone/ATF, AeroKroil, Liquid Wrench, PB Blaster, Royal Purple, and WD-40.

torque

Torque required to loosen the rusty bolt, which was measured in foot-pounds.

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)