penetrating_oil | R Documentation |
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.
penetrating_oil
A data frame with 30 observations on the following 2 variables.
The different treatments tried:
none
(control), Heat
(via blow torch), Acetone/ATF
,
AeroKroil
, Liquid Wrench
, PB Blaster
, Royal
Purple
, and WD-40
.
Torque required to loosen the rusty bolt, which was measured in foot-pounds.
https://www.youtube.com/watch?v=xUEob2oAKVs
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)
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