Each person who came to the clinic was screened for depression. Those who were diagnosed as "moderately depressed" were invited to participate in a treatment comparison study we were conducting. One of the IVs is the therapy condition, whether patients received cognitive-behavioral therapy (CBT), art therapy, or a support group control. Because of ethical concerns, patients were not randomly assigned to treatment conditions. Rather, each was permitted to choose which treatment they would receive. In addition, each patient was permitted to decide when they would begin treatment, in the Summer or Winter. As well as collecting the DV score (rating of depression, bigger scores indicating more depression), after 18 weeks of therapy, the researchers also recorded the initial depression score for each patient. The psychologist generated the following output from their analysis:
## Anova Table (Type III tests)
##
## Response: DepressionRating
## Sum Sq Df F value Pr(>F)
## (Intercept) 2097759 1 44.9959 1.575e-09 ***
## InitialDepression 19183 1 0.4115 0.5228
## Therapy 92192 2 0.9887 0.3760
## StartTherapy 26829 1 0.5755 0.4500
## Therapy:StartTherapy 71879 2 0.7709 0.4656
## Residuals 4289140 92
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1