A graduate student realized that the depression study above in Question 4 should have had a placebo condition in which a third group was given a pill just as the people in the Drug condition were, but where the pill was not Drug D (e.g., a sugar pill). So she designed a new experiment with three conditions -- Drug, No Drug, and Placebo. To perform the experiment, the graduate student randomly assigned 18 people into the three groups so that each group has 6 people. After one month of treatment, all 18 people were asked to rate on a scale from 1 to 7 how depressed they felt, where 1 = not depressed at all and 7 = very depressed. The following are the data:
A graduate student realized that the depression study above in Question 4 should have had a placebo condition in which a third group was given a pill just as the people in the Drug condition were, but where the pill was not Drug D (e.g., a sugar pill). So she designed a new experiment with three conditions -- Drug, No Drug, and Placebo. To perform the experiment, the graduate student randomly assigned 18 people into the three groups so that each group has 6 people. After one month of treatment, all 18 people were asked to rate on a scale from 1 to 7 how depressed they felt, where 1 = not depressed at all and 7 = very depressed. The following are the data:
| Drug | No Drug | Placebo |
|---|---|---|
| 2 | 4 | 5 |
| 3 | 5 | 5 |
| 4 | 5 | 6 |
| 4 | 4 | 5 |
| 2 | 6 | 4 |
| 3 | 6 | 5 |
| nD = 6 | nND = 6 | nplacebo = 6 |
| MD = 3 | MND = 5 | Mplacebo = 5 |
Using an α-level of .05, perform an Analysis of Variance (ANOVA) to determine whether there is a difference among the three conditions. Specifically, answer the following questions:
- What is the within condition degrees of freedom, dfwithin?
- What is the within condition sum of squares, SSwithin?
- What is the within condition
mean squares, MSwithin? - What is the between condition degrees of freedom, dfbetween?
- What is the between condition sum of squares, SSbetween?
- What is the between condition mean squares, MSbetween?
- Calculate the F-value for this experiment.
- Using Table F, choose the appropriate critical value of F for this problem.
- Based on the relationship between the value of F you calculated in (7) and the critical value of F you chose in (8), can the researcher conclude that there is a difference among the three conditions?
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