Question

The following results are from an independent-measures, two factor study. Be careful that this is a 2x3 design. You are expected to extend your knowledge on 2x2 design to a 2x3 factorial design.

The study:

Consider an experiment designed to investigate the effectiveness of therapy for the treatment of anxiety or fear. Two kinds of therapy (systematic desensitization, counter conditioning) as well as a counseling-only control condition are included. The therapy and counseling programs have been conducted over a number of sessions and the investigator asks whether more sessions might bring further improvements. The goal then is to compare two treatment lengths: the original and an extended version. For convenience, these two lengths are referred to as “Short” and “Long.” Participants’ well-being scores are measured; the larger the score, the more beneficial the treatment. Data are given in the table below. Answer the following questions using this data.

Form of Therapy	Counseling		Systematic Desensitization		Counter-Conditioning
Duration of Therapy	Short	Long	Short	Long	Short	Long
	10	13	5	0	6	3
	11	14	6	2	9	3
	12	7	3	4	5	4
	9	8	7	7	4	5
	12	10	8	5	3	5
	13	9	10	1	9	6
	12	10	8	4	6	4
	13	11	7	2	8	2
	10	12	9	4	4	7
	8	16	7	1	6	1

1. What are the dependent and independent variables in this study?
2. How many levels does each independent variable have and what are they?
3. State the hypotheses for each test.
4. Use a two-factor ANOVA with a=.05 to evaluate the main effects and interaction. For your answer, create a summary table and fill in the values. Do not show calculations here.
5. Based on what you found in ‘d’, what is your decision for each hypothesis test? Give F_obsand F_critfor each hypothesis test.
6. Plot cell means (you can draw this by hand if you don’t know how to do it using a computer) with form of therapy on the x-axis, participants’scoreson the y-axis, and duration of therapy as the grouping variable.
7. Run post-hoc analysis to sort out the interaction between two independent variables (simple effects analysis).
8. Based on your decision on the main effects and interaction, interpret the results. The interaction should have come out significant, so interpret accordingly! Here, I am not asking you to write a conclusion as it would appear in a research paper. I am simply asking you to interpret the results in your own words. The answer to this question should not take more than 5-6 simple sentences. If you are writing more than that, you are being redundant!

Answer 1

Note - a to e has been solved.

What are the dependent and independent variables in this study?
Dependent variable : Participants wellbeing scores
Independent variable : Form of therapy and Duration of therapy

How many levels does each independent variable have and what are they?

Form of therapy - 3 levels - Counseling
Systematic Desensitization
Counter-Conditioning

Duration of Therapy
Short
Long

State the hypotheses for each test.

Hypothesis 1
Ho : The mean well being due to the 3 forms of therapy is equal.
H1 : The mean well being due to the 3 forms of therapy is not equal

Hypothesis 2

Ho: The mean well being due to the duration of therapy is equal.
H1: The mean well being due to the duration of therapy is not equal.

Hypothesis 3
H0 : The form of therapy is independent of the duration of therapy.
H1: The form of therapy is not independent of the duration of therapy.

Use a two-factor ANOVA with a=.05 to evaluate the main effects and interaction. For your answer, create a summary table and fill in the values. Do not show calculations here.

Put the data in excel as shown.

Select Two factor anova without replication from the data analysis tab and input the data as shown.

The output will be presented as follows.

Based on what you found in ‘d’, what is your decision for each hypothesis test? Give Fobsand Fcritfor each hypothesis test.

Hypothesis 3 (Interaction)
H0 : The form of therapy is independent of the duration of therapy.
H1: The form of therapy is not independent of the duration of therapy.

From the table above, we see the pvalue for the interaction pvalue = 0.01, which is smaller than 0.05, hence we reject the null hypothesis and conclude that the interaction between form of therapy and duration is significant and they are not independent of each other.

Since the interaction effect is significant we do not investigate the other two hypotheses.
However, both the pvalue of the main effect are less than 0.05, hence they are significant.