A study is conducted to compare gas mileage for 3 competing...

A study is conducted to compare gas mileage for 3 competing brands of gasoline. Four different automobile models of varying size are randomly selected. The data, in miles per gallon, follow. The order of testing is random for each model. $$\begin{array}{cccc} & {\text { Gasoline Brand }} \\ { } \text { Model } & A & B & C \\ \hline A & 32.4 & 35.6 & 38.7 \\ B & 28.8 & 28.6 & 29.9 \\ C & 36.5 & 37.6 & 39.1 \\ D & 34.4 & 36.2 & 37.9\end{array}$$ (a) Discuss the need for the use of more than a single model of car. (b) Consider the ANOVA from the SAS printout in Figure 13.17 on page $578 .$ Does brand of gasoline matter? (c) Which brand of gasoline would you select? Consult the result of Duncan's test.

A study is conducted to compare gas mileage for 3 competing brands of gasoline. Four different automobile models of varying size are randomly selected. The data, in miles per gallon, follow. The order of testing is random for each model. $$\begin{array}{cccc} & {\text { Gasoline Brand }} \\
{ } \text { Model } & A & B & C \\
\hline A & 32.4 & 35.6 & 38.7 \\
B & 28.8 & 28.6 & 29.9 \\
C & 36.5 & 37.6 & 39.1 \\
D & 34.4 & 36.2 & 37.9\end{array}$$ (a) Discuss the need for the use of more than a single model of car.
(b) Consider the ANOVA from the SAS printout in Figure 13.17 on page $578 .$ Does brand of gasoline matter?
(c) Which brand of gasoline would you select? Consult the result of Duncan's test.

Key Concepts

Blocking in Experimental Design

Blocking involves grouping experimental units that are similar in ways that are expected to affect the response variable. In this study, using different models of automobile serves as blocks to reduce the variability due to differences in car performance. This approach isolates the effect of gasoline brand by accounting for the inherent variation among different car models.

Randomization

Randomization is the process of assigning treatments to experimental units in a random manner to prevent systematic bias. In the study, randomizing the order of gasoline brand testing for each car model minimizes potential order effects and confounding variables, ensuring that the treatment effects are not confounded with other extraneous factors.

Analysis of Variance (ANOVA)

ANOVA is a statistical method used to compare means across multiple groups by partitioning the overall variability into components attributable to different sources. In this context, one-factor or possibly two-factor ANOVA is applied to determine if there are significant differences in gas mileage among the different gasoline brands while accounting for the variability among car models.

Multiple Comparison Procedures

Multiple comparison procedures, such as Duncan's test in this instance, are used after obtaining a significant ANOVA result to identify which specific group means are different from each other. Duncan's test helps in ranking the gasoline brands by comparing their mean performances, thereby assisting in selecting the brand that offers the best gas mileage.

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