Question

Depressed patients were randomly assigned to one of three groups: a placebo group, a group that received a moderate dose of the drug, and a group that received a high dose of the drug. After four weeks of treatment, the patients completed the Beck Depression Inventory. The higher the score, the more depressed the patient.

We are now also interested if a patient's weight has an effect on the drug's effectiveness. Patients were categorized as either underweight, overweight, or 'medium weight'.  These revised data are presented below. Use the Microsoft Excel "Anova Single-Factor" Data Analysis tool to conduct a 2-way ANOVA test for the data in the following table:

	Placebo	Moderate Dose	High Dose
underweight	42	22	13
underweight	52	19	14
medweight	41	31	12
medweight	41	21	19
overweight	39	8	10
overweight	33	23	0

1. What are your three null hypotheses in this study?
2. What are your three corresponding alternate hypotheses? Use the phrase "at least one" in each of your hypothesis statements.
3. What level of significance did you choose and why?

Answer 1

1. What are your three null hypotheses in this study?

H0: There is no main effect of weight

H0: There is no main effect of the drug

H0: There is no interaction effect

1. What are your three corresponding alternate hypotheses? Use the phrase "at least one" in each of your hypothesis statements.

Ha: There is a main effect of at least one weight

Ha: There is a main effect of at least one drug

Ha: There is at least one interaction effect

1. What level of significance did you choose and why?

The level of significance is 0.05 because it is the most appropriate level for rejecting the null hypothesis when it is true.