In-Class Exercise
A driver’s ability to detect highway signs is an important consideration in highway safety. In his dissertation Highway Construction Safety and the Aging Driver, Solomon Younes investigated the distance at which drivers can first detect highway caution signs. This distance is called the detection distance. An experiment was conducted to determine the effects that sign size and sign material have on detection distance. Four drivers were randomly selected for each combination of sign size (small, medium, large), and sign material (1, 2, 3). Each driver covered the same stretch of highway at a constant speed during the same time of day, and the detection distance (in feet) was determined for the driver’s assigned caution sign.
1. What is the response variable for this experiment?
2. What are the 2 factors for this experiment?
3. What are the levels for the 2 factors?
4. The following table presents the means for the different factor/level combinations. Based on this table, which combination of factor levels gives a sign that can be detected most quickly (e.g., has the longest detection distance)?
Large signs made of material 1
(3365.2)
Size
|
1 |
2 |
3 |
|
Small
|
2485.8 |
2158.5 |
1670.2 |
2104.8 |
|
Medium |
2803.8 |
2380.8 |
2333.2 |
2505.9 |
Large
|
3365.2 |
3029.5 |
2744.0 |
3046.3 |
|
|
2884.9 |
2522.9 |
2249.2 |
|
5. The ANOVA table for this experiment is given below. Is there a significant interaction between size and material? Give evidence for your answer.
No, there is not a significant interaction since the p-value for the interaction term is 0.4090, which is greater than 0.05.
SIZE 2 5356373 2678187 50.91 0.0001
MATERIAL 2 2440644 1220322 23.20 0.0001
SIZE*MATERIAL 4 217044 54261 1.03 0.4090
Error 27 1420314 52604
6. Is either of the main effects significant? Why or why not?
Both of the main effects are
significant since the p-value for each main effect is << 0.05.
