3.3. Example Problem Fixed Effect One-Way/Single-Factor Completely Randomized Design Analysis of Variance ANOVA
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[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. What is the treatment in this experiment?
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[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. What conclusion would you make from the Fisher pairwise comparisons?
10 points
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[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. What is the factor type in this experiment?
10 points
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[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. What STATISTICAL conclusion would you make after analyzing the data with respect to the discomfort rating using an appropriate statistical method?  
10 points
Clear selection
 [Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. What would be the most appropriate statistical method for this experiment?
10 points
Clear selection
[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. What STATISTICAL conclusion would you make after analyzing the data with respect to the speed using an appropriate statistical method?  
10 points
Clear selection
[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. What is the experimental unit in this experiment?
10 points
Clear selection
[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. Experimental random errors occur from?
10 points
Clear selection
[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. What CONTEXTUAL conclusion would you make after analyzing the data with respect to the speed using an appropriate statistical method?  
10 points
Clear selection
[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. What CONTEXTUAL conclusion would you make after analyzing the data with respect to the average discomfort rating using an appropriate statistical method?  
10 points
Clear selection
[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. What is the factor in this experiment?
10 points
Clear selection
[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. What is the dependent variable in this experiment?
10 points
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[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. What are the levels in this experiment?
10 points
Clear selection
[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. What is sample size in this experiment?
10 points
Clear selection
[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. Experimental systematic errors occur from?
10 points
Clear selection
[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. What is the independent variable in this experiment?
10 points
Clear selection
[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. Which tire size would you recommend considering both speed and discomfort rating according to the Tukey pairwise comparisons results?
10 points
Clear selection
[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. What conclusion would you NOT make from the Tukey/Fisher pairwise comparisons?
10 points
Clear selection
[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. What is the response variable in this experiment?
10 points
Clear selection
[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. In a group/team cycling, generally cyclists draft behind other cyclists and keep rotating the group members so that one person only has to be in the front for a very short period of time to fight the wind. Cycling speed significantly gets improved by rotating like this. Therefore, the overall performance is dependent on each other. Which assumption required for the analysis is violated in this cycling experiment.
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[Data File Sheet Name: DOEM 3.2]. To determine the best tire size for long-distance road cycling, a tire manufacturer is comparing the three commonly used tire sizes (23mm, 25mm and 28mm) for the road cycling. The experimenter selected 90 randomly chosen cyclists with very similar characteristics, including their body weight, height, power, etc., which can be comparable to identical but independent twins (identical and independent experimental units). The experimenter collected a long-distance 50-mile training ride data, including both the average speed and the subjective rating of their perceived discomfort for all three tire sizes. What conclusion would you NOT make from the Tukey pairwise comparisons?
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