7.54 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. 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: Heat WD-40 Royal Purple PB Blaster Liquid Wrench Aerokroil Acetone/ATF Acetone/ATF AeroKroil none Heat Liquid Wrench 100 110 120 130 Torque Required to Loosen Rusty Bolt, in Foot-Pounds (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. none PB Blaster Royal Purple 90 Df Sum Sq Mean Sq F value treatment 7 3603.43 514.78 Residuals 22 2812.80 127.85 4.03 (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 0.2026 0.0308 0.1542 0.0027 0.8723 0.0020 0.0017 Pr(>F) 0.0056 0.0476 0.0025 0.5580 140 PB Blaster 0.3294 0.7551 0.0050 0.0053 0.6371 Royal Purple WD-40 0.3744 0.6883 0.0059 0.0065 0.5751 0.9286 0.8000 0.5222 0.5143 0.0096 0.0117 0.4180 0.7318 (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.
7.54 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. 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: Heat WD-40 Royal Purple PB Blaster Liquid Wrench Aerokroil Acetone/ATF Acetone/ATF AeroKroil none Heat Liquid Wrench 100 110 120 130 Torque Required to Loosen Rusty Bolt, in Foot-Pounds (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. none PB Blaster Royal Purple 90 Df Sum Sq Mean Sq F value treatment 7 3603.43 514.78 Residuals 22 2812.80 127.85 4.03 (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 0.2026 0.0308 0.1542 0.0027 0.8723 0.0020 0.0017 Pr(>F) 0.0056 0.0476 0.0025 0.5580 140 PB Blaster 0.3294 0.7551 0.0050 0.0053 0.6371 Royal Purple WD-40 0.3744 0.6883 0.0059 0.0065 0.5751 0.9286 0.8000 0.5222 0.5143 0.0096 0.0117 0.4180 0.7318 (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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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7.54 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. 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:
Heat
WD-40
Royal Purple
PB Blaster
Liquid Wrench
AeroKroil -
Acetone/ATF
Acetone/ATF
AeroKroil
none
Heat
Liquid Wrench
90
100
110
120
130
Torque Required to Loosen Rusty Bolt, in Foot-Pounds
(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
treatment 7 3603.43 514.78
Residuals 22 2812.80 127.85
4.03
none
PB Blaster
Royal Purple
(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?
Pr(>F)
0.0056
AeroKroil Heat Liquid Wrench none
0.2026 0.0308
0.0476
0.1542
0.0027
0.0025
0.8723
0.5580
0.0020
0.0017
140
PB Blaster Royal Purple WD-40
0.3744
0.6883
0.0059
0.0065
0.5751
0.9286
0.8000
0.3294
0.7551
0.0050
0.0053
0.6371
0.5222
0.5143
0.0096
0.0117
0.4180
0.7318
(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.
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