Question

Thirty-two patients suffering from depression were randomly assigned to one of four drug treatment groups: 0 mg (placebo), 1 mg, 2 mg, or 3 mg of antidepressant drug. The table below summarizes the patients' improvement scores in personal adjustment following one month of drug therapy.

	Treatment
	1 (0 mg)	2 (1 mg)	3 (2 mg)	4 (3 mg)
n	8	8	8	8
sum	43	57	102	92
means	5.38	7.13	12.75	11.50

Source	SS	df	MS	F
Between (A)	(1)	(2)	(5)	(7)
Within (Error)	528.24	(3)	(6)
Total	822.87	(4)

1. What are the independent and dependent variables? (2)
2. Above is a partially completed ANOVA summary table. Each missing cell is labelled [e.g., (1), (2), (3)]. Use the space below to provide the missing components (make sure to properly identify each one). Provide a conclusion as you normally would. (13)
3. Let's say you had planned to use the most powerful comparison test possible to determine whether or not the following contrasts are significant:

Contrast 1: Treatment 1 vs. treatment 2

Contrast 2: Treatment 3 vs. treatment 4

Contrast 3: Treatments 1 and 2 vs. treatment 3 and 4

WITHOUT doing the actual analysis, could one do this test, indicating why or why not? (7)

Answer 1

Answer:

Given Data

(a) What are the independent and dependent variables.

The independent variable is the four treatment groups. The dependent variable is the improvement scores.

(b)  Above is a partially completed ANOVA summary table. Each missing cell is labelled. Use the space below to provide the missing components .

Source	SS	df	MS	F
Between	294.63	3	98.21	5.20574
Error	528.24	28	18.86571
Total	822.87	31

The p-value is 0.0055.

Since the p-value (0.0055) is less than the significance level (0.05),

we can reject the null hypothesis.

Therefore, we can conclude that there is a significant difference between the four treatment groups.

(c)  Let's say you had planned to use the most powerful comparison test possible to determine whether or not the following contrasts are significant:

Contrast 1: Treatment 1 vs. treatment 2

Contrast 2: Treatment 3 vs. treatment 4

Contrast 3: Treatments 1 and 2 vs. treatment 3 and 4

There is no significant difference.

There is no significant difference.

There is a significant difference.

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