Question

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 7 7 9 4 9 5 6 8 7 Night 5 6 9 8 8 7 6 7 6 7 5 8 4 9 7 3 8 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 1 Intensity 2 Time of day × Intensity 2 Error 30 Total 90.889 35 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.

Answer 1

(a)

Source	SS	df	MS	F
Factor 1	1.00	1	1.00	0.43
Factor 2	19.39	2	9.69	4.15
Interaction	0.50	2	0.25	0.11
Error	70.00	30	2.33
Total	90.89	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) The critical value is 2.47 for each pairwise comparison.

The output is:

			Factor 2
	Means:
		Low	Medium	High
	Morning	5.3	6.5	7.0	6.3
Factor 1	Night	5.5	7.2	7.2	6.6
		5.4	6.8	7.1	6.4
	6	replications per cell
ANOVA table
Source	SS	df	MS	F	p-value
Factor 1	1.00	1	1.00	0.43	.5177
Factor 2	19.39	2	9.69	4.15	.0255
Interaction	0.50	2	0.25	0.11	.8987
Error	70.00	30	2.33
Total	90.89	35
Post hoc analysis
p-values for pairwise t-tests for Factor 2
		Low	Medium	High
		5.4	6.8	7.1
Low	5.4
Medium	6.8	.0304
High	7.1	.0121	.6913
Tukey simultaneous comparison t-values (d.f. = 30)
		Low	Medium	High
		5.4	6.8	7.1
Low	5.4
Medium	6.8	2.27
High	7.1	2.67	0.40
critical values for experimentwise error rate:
		0.05	2.47
		0.01	3.15