Correlation and Regression Questions

 

 

1. Briefly explain why a related samples (or repeated measures) design has more statistical power (i.e., is more likely to reject H₀, if there is a true difference in the population) than a comparable independent samples (or between subjects) design (2 points).

2. Briefly explain why conducting multiple t-tests will result in an inflated experimentwise alpha level, compared to using ANOVA. (2 points)

3. A researcher examines whether a “sensitization” intervention decreases cigarette smoking. A random sample of 8 smokers is selected and the average number of cigarettes smoked per day is determined. The individuals are then sensitized to the effects of smoking by having them participate in a number of exercises (e.g., they talk to a terminally ill lung cancer patient). Eight days later, the participants are asked to report the number of cigarettes they smoked the previous day. The data are as follows:

BeforeOne week later

19 15

22 7

32 31

17 10

37 28

20 12

23 23

• 17

Did sensitization cause a significant reduction in smoking? (a) Test this hypothesis using the appropriate statistical test, showing the four steps and all your work; and (b) calculate an estimate of effect size using Cohen’s d. Use α = .05. (6 points)

4. Hollon, Thase, and Markowitz (2002) analyzed the effectiveness of different treatments for depression, including psychodynamic therapy, interpersonal therapy, and cognitive-behavioural therapy. The data below represent the outcomes for three groups of patients who each received one of these treatments (the scores reflect the extent to which the person responded to the treatment, with higher numbers indicating greater efficacy of treatment).

Psychodynamic Interpersonal Cognitive-Behavioural

37 49 36

30 52 49

22 41 42

29 39 42

22 50 37

(a) Determine if the treatment outcomes differ, using the appropriate statistical test and making sure that you show all your work and the 4 steps of hypothesis testing (use a = .05); (b) perform a post-hoc comparison of treatment means, if necessary, using Tukey’s HSD test, and make a conclusion about which means are significantly different from each other (10 points)