Question

Further to the legalization of Cannabis in Canada, the Ontario Ministry of Transportation (OMT) is preparing an advertising campaign to discourage impaired driving due to the use of cannabis products. The campaign will target the most dangerous combinations of THC levels and time since last intake on driving competencies. As a recent Telfer graduate with a passion for statistics, you’ve been hired by the OMT to manage this project with the assistance of a research agency. You recruit 60 individuals and assign them randomly to 4 different treatment groups of interest. Subjects must consume a certain quantity of cannabis and then go to a virtual simulator room after a certain period of time to test their driving abilities on a scale totaling 30 points. Score data for the different treatment groups can be found in the data below at the end of the questions

a) This study consists of what kind of experiment? Describe its main components and explain how it differs from an observational study.

b)Make a side-by-side boxplot of the data and explain if the similar variance and the nearly normal conditions for conducting an ANOVA seem to be satisfied.

c) In addition to a side-by-side boxplot, what other graphs can you use to check if the assumptions/conditions for using an ANOVA are satisfied? (Note: you don’t need to produce these graphs; just explain how you would produce them.)

d)Calculate the sample variance for each treatment group and then use it to calculate the pooled variance manually. Check to see if your pooled variance agrees with the MSE displayed on the partial ANOVA table in part e) below.

e) Fill in manually the correct values for the missing values in the ANOVA table below. Show your computations (maximum of 2 decimal places).

ANOVA
source of variation	SS	df	MS	F	p-value
Between Groups	X	3	X	X	X
Within Groups	X	X	10.47
Total	786.18	59

f) Using the one-way ANOVA in e) above, test if there is a significant difference in the true mean score between the 4 treatment groups using the critical value approach and a 5% significance level. Make sure you follow all the steps for hypothesis testing indicated in the Instructions section, show your computations, and state the business significance of your conclusion.

g) Use the Bonferroni multiple comparison method to determine which population means differ at α = 0.05. Show your computations.

h) Perform a Kruskal-Wallis non-parametric test to determine whether there is a difference among the four-intake group (treatment group) scores. Use a 5% significance level and the critical value approach. You can use Excel or Minitab for your calculations but remember to show all the steps of your hypothesis test. Is your conclusion consistent with your results in f) above?

Score on Driving Test after Intake (Max.30)
Intake/Treatment Groups
Light Dose-2 hours Wait	Light Dose-4 hours Wait	Heavy Dose- 2 hours Wait	Heavy Dose- 4 hours Wait
28	27	27	24
30	27	25	24
26	27	23	24
23	25	19	23
23	29	21	21
20	24	23	19
26	30	23	21
25	28	19	25
24	29	23	23
19	20	18	14
22	21	15	17
25	22	21	20
24	24	19	20
22	23	17	24
20	22	15	25

Answer 1

a. This is a field experiment. The components are:

Independent variable: cannabis products

Dependent variable: Driving abilities

Experimental groups: 4 experimental groups:

1. Light Dose-2 hours Wait, 2. Light Dose-4 hours Wait, 3. Heavy Dose- 2 hours Wait 4. Heavy Dose- 4 hours Wait

Subjects/Experimental units: 60 individuals

Response: driving abilities on a scale totaling 30 points

Since here we apply 4 treatments (i.e. Light Dose-2 hours Wait, Light Dose-4 hours Wait, Heavy Dose- 2 hours Wait, Heavy Dose- 4 hours Wait) to a group and recording the effects, so it is an experiment and not an observational study.

2.

From above boxplots, we see that width boxes are more or less same, so we can assume that variances of all 4 groups are almost same.

c.

From above probability plot we see that assumption of normality holds.

Test for Equal Variances: Driving Ability versus Treatment group

95% Bonferroni confidence intervals for standard deviations

Treatment group N Lower StDev Upper
Heavy Dose- 2 hours Wait 15 2.38172 3.52272 6.39218
Heavy Dose- 4 hours Wait 15 2.15021 3.18030 5.77084
Light Dose-2 hours Wait 15 2.04754 3.02844 5.49528
Light Dose-4 hours Wait 15 2.15628 3.18927 5.78712

Bartlett's Test (Normal Distribution)
Test statistic = 0.34, p-value = 0.953

Since P-value=0.953>0.05 so assumption of equal variances also holds.

d.

Variable Variance
Light Dose-2 hours Wait 9.171=s12
Light Dose-4 hours Wait 10.171=s22
Heavy Dose- 2 hours Wait 12.410=s32
Heavy Dose- 4 hours Wait 10.114=s42

One-way ANOVA: Driving Ability versus Treatment group

Source DF SS MS F P
Treatment group 3 200.0 66.7 6.37 0.001
Error 56 586.1 10.5
Total 59 786.2

e.

Source DF SS MS F P
Treatment group 3 200.0 66.7 6.37 0.00
Error 56 586.1 10.5
Total 59 786.2

f. Critical value=F0.05,3,56=2.77

Since F-value=6.37>Critical value so there is a significant difference in the true mean score between the 4 treatment groups.