Question

Question 2 (7 parts, 25 marks) Following your initial analysis in Question 1 above, you think that, in addition to cannabis use, road conditions may also affect driving abilities and contribute to an increased risk of road accidents. You suggest that further testing be made using 5 different road-condition scenarios in the virtual driving simulator. Your proposal is accepted and a new group of 60 individuals are solicited to participate in the study and are randomly assigned to one of the various treatment groups. Score data for the different treatment groups can be found in the Assign3Data.xlsx file. a) [4 marks] Identify the experimental design and determine the number of treatments, experimental units and replicates. b) 15 marks] Plot the residuals against the fitted values corresponding to the two-way ANOVA model for this experiment. What two key model assumptions can be examined with this plot and do they appear to be warranted?

Answer 1

(a) The experimental design is the Two-Way Factorial Design. The number of treatments is two, experimental units are different road-condition scenarios and Treatment Groups, and replicates are 3.

(b) The residual plot is:

Versus Fits (response is C3) Residual -2.5 - 16 18 20 22 24 Fitted Value 26 28 30

There is no presence of homoscedasticity.

There is equal variance among the groups.

(c) Significant interaction effect between cannabis intake and road conditions;

No, there is no significant interaction effect between cannabis intake and road conditions.

Significant main effect of the cannabis intake factor (if warranted);

Yes, there is a significant main effect of the cannabis intake factor.

Significant main effect of the road conditions factor (if warranted).

Yes, there is a significant main effect of the road conditions factor.

ANOVA table
Source	SS	df	MS	F	p-value
Factor 1	328.40	4	82.100	20.61	2.77E-09
Factor 2	202.47	3	67.489	16.94	2.95E-07
Interaction	92.53	12	7.711	1.94	.0589
Error	159.33	40	3.983
Total	782.73	59

(d) The interaction plot is:

Interaction Plot for C3 Data Means Scenarios - Scenario-1 Scenario-2 Scenario-3 Scenario-4 - Scenario-5 - Mean --- - + -- Y Heavy Dose - 2 hours Wait Heavy Dose- 4 hours Wait Light Do Se-2 hours Wait Light Dose-4 hours Wait Intake Treatment Groups

There is an interaction between cannabis intake and road conditions impacting on driving scores.

(e)

Means:
	Light Dose-2 hours Wait	Light Dose-4 hours Wait	Heavy Dose- 2 hours Wait	Heavy Dose- 4 hours Wait
Scenario-1	28.0	27.0	25.0	24.0	26.0
Scenario-2	22.0	26.0	21.0	21.0	22.5
Scenario-3	25.0	29.0	21.7	23.0	24.7
Scenario-4	22.0	21.0	18.0	17.0	19.5
Scenario-5	22.0	23.0	17.0	23.0	21.3
	23.8	25.2	20.5	21.6	22.8

Scenario-3 and Light Dose-4 hours Wait have the highest average driving scores.

Scenario-5 and Heavy Dose- 2 hours Wait have the lowest average driving scores.