A researcher studying depression is interested in whether a new medication is effective in treating depressive symptoms among patients at an outpatient clinic. Fifty individuals are selected for the study, who are new admits to the clinic. Twenty-five are randomly assigned to the medication condition, and 25 are assigned to the condition that gets a sugar pill (placebo). After 8 weeks, participants are administered the Beverly Depression Scale, which assesses the core symptoms of clinical depression.

As in the above example (#5) a researcher is interested in the treatment of depression, however her sample is half the size. She has 25 subjects and is interested in the effectiveness of a new medication, called Fixital. She administers the Beverly Depression Scale to participants before starting the medication, and then re-administers this depression scale to the 25 subjects after they have been on the medication for 8 weeks.

As in the two above examples, a researcher is interested in the treatment of depression. In this instance, his sample size is much larger (150 volunteer patients who have just enrolled in a treatment study). In this case, they are randomly assigned to three different groups: medication (fixital), sugar pill/placebo, and individual counseling (12 weekly counseling sessions using a treatment manual). After 12 weeks in the study, participants are administered the Beverly Depression Scale, with the intent of determining if any of the interventions are effective, and to what degree (e.g. is one approach better than the rest). Which statistical test would he use to analyze the data?