Seasonal affective disorder (SAD) is a type of depression during seasons with less daylight (e.g., winter months). One therapy for SAD is phototherapy, which is increased exposure to light used to improve mood. A researcher tests this therapy by exposing a sample of patients with SAD to different intensities of light (low, medium, high) in a light box, either in the morning or at night (these are the times thought to be most effective for light therapy). All participants rated their mood following this therapy on a scale from 1 (poor mood) to 9 (improved mood). The hypothetical results are given in the following table.
| Light Intensity | ||||
|---|---|---|---|---|
| Low | Medium | High | ||
| Time
of Day |
Morning | 5 | 5 | 7 |
| 6 | 6 | 8 | ||
| 4 | 4 | 6 | ||
| 6 | 7 | 9 | ||
| 5 | 9 | 5 | ||
| 6 | 8 | 8 | ||
| Night | 5 | 6 | 9 | |
| 8 | 8 | 7 | ||
| 6 | 7 | 6 | ||
| 6 | 5 | 8 | ||
| 4 | 9 | 7 | ||
| 3 | 7 | 6 | ||
(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test. (Round your answers to two decimal places. Assume experimentwise alpha equal to 0.05.)
|
Source of Variation |
SS | df | MS | F |
|---|---|---|---|---|
| Time of day | ||||
| Intensity | ||||
| Time
of day × Intensity |
||||
| Error | ||||
| Total |
State the decision for the main effect of the time of day.
Retain the null hypothesis.Reject the null hypothesis.
State the decision for the main effect of intensity.
Retain the null hypothesis.Reject the null hypothesis.
State the decision for the interaction effect.
Retain the null hypothesis.Reject the null hypothesis.
(b) Compute Tukey's HSD to analyze the significant main effect.
The critical value is for each pairwise comparison.
Summarize the results for this test using APA format.
(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test. (Round your answers to two decimal places. Assume experimentwise alpha equal to 0.05.)
| Source | SS | df | MS | F |
| Time of day | 0.25 | 1 | 0.25 | 0.12 |
| Intensity | 22.17 | 2 | 11.08 | 5.21 |
| Time
of day × Intensity |
0.50 | 2 | 0.25 | 0.12 |
| Error | 63.83 | 30 | 2.13 | |
| Total | 86.75 | 35 |
State the decision for the main effect of the time of day.
Retain the null hypothesis.
State the decision for the main effect of intensity.
Reject the null hypothesis.
State the decision for the interaction effect.
Retain the null hypothesis.
(b) Compute Tukey's HSD to analyze the significant main effect.
The critical value is 1.47 for each pairwise comparison.
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