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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?

Detection distance

 

2.       What are the 2 factors for this experiment?

Sign size and sign material

 

3.       What are the levels for the 2 factors?

Sign size:  small, medium, large           Sign material: 1, 2, 3

 

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)

 

 

 

Sign Material

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.

 

 

 

 

Source                         DF       SS                    MS                   F                      P-val

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.