A researcher conducted an experiment to test the effects of running 3 different types of gasoline with 3 possible types of additive on the mileage obtained. The experiment assumed that there is an interaction between gasoline type and the type of additive, hence, a two-factor ANOVA was employed in the data analysis. It was decided to run 36 motors – 4 in each factor level combinations. The following are the analysis results MEAN ADDITIVE 1 ADDITIVE 2 ADDITIVE 3 GAS TYPE 1 125.825 130.775 128.275 128.2917 GAS TYPE 2 127 133.6 137.825 132.8083 GAS TYPE 3 126.35 132.5 123 127.2833 126.3917 132.2917 129.7 129.4611 Analysis of Variance Table Df Sum Sq Mean Sq F Value Pr(>F) factor(gas.type) 2 207.7706 103.8853 11.08482 0.000306 factor(additive) 2 209.8872 104.9436 11.19775 0.000287 factor(gas.type):factor(additive) 4 262.9678 65.74194 7.01483 0.000523 Residuals 27 253.04 9.371852 NA NA a.) Is there a significant interaction between the type of gasoline and the type of additive? Why? b.) What does the result on the test for significant interaction imply? c.) Say you are to choose between the three gasoline types, regardless of the type of additive used and considering all other factors constant. Which gasoline would you prefer for your motor and why?
A researcher conducted an experiment to test the effects of running 3 different types of gasoline with 3 possible types of additive on the mileage obtained. The experiment assumed that there is an interaction between gasoline type and the type of additive,
hence, a two-factor ANOVA was employed in the data analysis. It was decided to run 36 motors – 4 in each factor level combinations. The following are the analysis results
MEAN
ADDITIVE 1 | ADDITIVE 2 | ADDITIVE 3 | ||
GAS TYPE 1 | 125.825 | 130.775 | 128.275 | 128.2917 |
GAS TYPE 2 | 127 | 133.6 | 137.825 | 132.8083 |
GAS TYPE 3 | 126.35 | 132.5 | 123 | 127.2833 |
126.3917 | 132.2917 | 129.7 | 129.4611 |
Analysis of Variance Table
Df | Sum Sq | Mean Sq | F Value | Pr(>F) | |
factor(gas.type) | 2 | 207.7706 | 103.8853 | 11.08482 | 0.000306 |
factor(additive) | 2 | 209.8872 | 104.9436 | 11.19775 | 0.000287 |
factor(gas.type):factor(additive) | 4 | 262.9678 | 65.74194 | 7.01483 | 0.000523 |
Residuals | 27 | 253.04 | 9.371852 | NA | NA |
a.) Is there a significant interaction between the type of gasoline and the type of additive? Why?
b.) What does the result on the test for significant interaction imply?
c.) Say you are to choose between the three gasoline types, regardless of the type of additive used and considering all other factors constant. Which gasoline would you prefer for your motor and why?
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