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.
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, andWD-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)
#> Analysis of Variance Table
#>
#> Response: torque
#> Df Sum Sq Mean Sq F value Pr(>F)
#> treatment 7 3603.4 514.78 4.0263 0.005569 **
#> Residuals 22 2812.8 127.85
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
# 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")
}
}
}
#> 0.3 - AeroKroil Heat
#> 0.3 - AeroKroil Liquid Wrench
#> 0.3 - Heat none
#> 0.3 - Liquid Wrench none
# Smallest p-value using Bonferroni
min(2 * K * pt(-abs(diff / se), df))
#> [1] 0.2030646
# Better pairwise comparison method.
anova(m1 <- aov(torque ~ treatment, data = penetrating_oil))
#> Analysis of Variance Table
#>
#> Response: torque
#> Df Sum Sq Mean Sq F value Pr(>F)
#> treatment 7 3603.4 514.78 4.0263 0.005569 **
#> Residuals 22 2812.8 127.85
#> ---
#> Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
TukeyHSD(m1)
#> Tukey multiple comparisons of means
#> 95% family-wise confidence level
#>
#> Fit: aov(formula = torque ~ treatment, data = penetrating_oil)
#>
#> $treatment
#> diff lwr upr p adj
#> AeroKroil-Acetone/ATF 10.500 -16.194618 37.1946185 0.8842366
#> Heat-Acetone/ATF -22.600 -55.294097 10.0940971 0.3327605
#> Liquid Wrench-Acetone/ATF -16.775 -43.469618 9.9196185 0.4458126
#> PB Blaster-Acetone/ATF 7.975 -18.719618 34.6696185 0.9699935
#> Royal Purple-Acetone/ATF 5.200 -21.494618 31.8946185 0.9975362
#> WD-40-Acetone/ATF 7.250 -19.444618 33.9446185 0.9822024
#> none-Acetone/ATF 11.800 -14.894618 38.4946185 0.8116953
#> Heat-AeroKroil -33.100 -65.794097 -0.4059029 0.0458145
#> Liquid Wrench-AeroKroil -27.275 -53.969618 -0.5803815 0.0428856
#> PB Blaster-AeroKroil -2.525 -29.219618 24.1696185 0.9999789
#> Royal Purple-AeroKroil -5.300 -31.994618 21.3946185 0.9972260
#> WD-40-AeroKroil -3.250 -29.944618 23.4446185 0.9998837
#> none-AeroKroil 1.300 -25.394618 27.9946185 0.9999998
#> Liquid Wrench-Heat 5.825 -26.869097 38.5190971 0.9985955
#> PB Blaster-Heat 30.575 -2.119097 63.2690971 0.0780794
#> Royal Purple-Heat 27.800 -4.894097 60.4940971 0.1354969
#> WD-40-Heat 29.850 -2.844097 62.5440971 0.0905238
#> none-Heat 34.400 1.705903 67.0940971 0.0344923
#> PB Blaster-Liquid Wrench 24.750 -1.944618 51.4446185 0.0823993
#> Royal Purple-Liquid Wrench 21.975 -4.719618 48.6696185 0.1600902
#> WD-40-Liquid Wrench 24.025 -2.669618 50.7196185 0.0986124
#> none-Liquid Wrench 28.575 1.880382 55.2696185 0.0302211
#> Royal Purple-PB Blaster -2.775 -29.469618 23.9196185 0.9999599
#> WD-40-PB Blaster -0.725 -27.419618 25.9696185 1.0000000
#> none-PB Blaster 3.825 -22.869618 30.5196185 0.9996572
#> WD-40-Royal Purple 2.050 -24.644618 28.7446185 0.9999949
#> none-Royal Purple 6.600 -20.094618 33.2946185 0.9895945
#> none-WD-40 4.550 -22.144618 31.2446185 0.9989414
#>