Torque on a rusty bolt. Project Farm is a YouTube channel that routinely compares different products. In one episode, the channel evaluated different options for loosening rusty bolts.40 Eight options were evaluated, including a control group where no treatment was given (“none” in the graph), to determine which was most effective. For all treatments, there were four bolts tested, except for a treatment of heat with a blow torch, where only two data points were collected. The results are shown in the figure below:
Torque Required to Loosen Rusty Bolt, in Foot−Pounds
90 100 110 120 130 140
(a) Do you think it is reasonable to apply ANOVA in this case?
(b) Regardless of your answer in part (a), describe hypotheses for ANOVA in this context, and use the table below to carry out the test. Give your conclusion in the context of the data.
Df Sum Sq Mean Sq F value Pr(>F)
treatment 7 3603.43 514.78 4.03 0.0056 Residuals 22 2812.80 127.85
(c) The table below are p-values for pairwise t-tests comparing each of the different groups. These p-values have not been corrected for multiple comparisons. Which pair of groups appears most likely to represent a difference?
AeroKroil Heat Liquid Wrench none PB Blaster Royal Purple WD-40 Acetone/ATF 0.2026 0.0308 0.0476 0.1542 0.3294 0.5222 0.3744 AeroKroil 0.0027 0.0025 0.8723 0.7551 0.5143 0.6883 Heat 0.5580 0.0020 0.0050 0.0096 0.0059 Liquid Wrench 0.0017 0.0053 0.0117 0.0065 none 0.6371 0.4180 0.5751 PB Blaster 0.7318 0.9286 Royal Purple 0.8000
(d) There are 28 p-values shown in the table in part (c). Determine if any of them are statistically significant after correcting for multiple comparisons. If so, which one(s)? Explain your answer.