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In-Class Exercise

 

A driverís 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 driverís 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.