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	4	5	7
		6	6	8
		4	4	6
		7	7	9
		5	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	2	3	4
Intensity	5	6	7	8
Time of day × Intensity	9	10	11	12
Error	13	14	15
Total	16	17

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.

EXPLAIN THE PROCESS, HOW TO..SS, DF, MS, F, VARIANCE?????

Answer 1

ANOVA table

Source	DF	SS	MS	F	P
Time of Day	1	1.00	1.00	0.43	0.518
Light Intensity	2	19.39	9.69	4.15	0.026
Interaction	2	0.50	0.25	0.11	0.899
Error	30	70.00	2.33
Total	35	90.8889

S = 1.528 R-Sq = 22.98% R-Sq(adj) = 10.15%

State the decision for the main effect of the time of day.

Ans: Retain the null hypothesis.

State the decision for the main effect of intensity.

Ans: Reject the null hypothesis.    

State the decision for the interaction effect.

Ans: Reject the null hypothesis.

    

The critical value is 3.44 for each pairwise comparison.

b)

Multiple Comparisons
Y Tukey HSD
(I) Light	(J) Light	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
					Lower Bound	Upper Bound
Low	Medium	-1.4167	.62361	.076	-2.9540	.1207
	High	-1.6667*	.62361	.031	-3.2040	-.1293
Medium	High	-.2500	.62361	.915	-1.7874	1.2874

Comment: The mean rate of mood in the levels Low and High of the Light intensity are significantly different at the 0.05 significance level.