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 SAD patients 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
		5	9	5
		6	8	8
	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
Intensity
Time of day × Intensity
Error
Total

Answer 1

Output using excel:

Anova: Two-Factor With Replication
SUMMARY	Low	Medium	High	Total
Morning
Count	6	6	6	18
Sum	33	39	43	115
Average	5.5	6.5	7.166667	6.388889
Variance	1.1	3.5	2.166667	2.486928
Night
Count	6	6	6	18
Sum	33	43	43	119
Average	5.5	7.166667	7.166667	6.611111
Variance	3.5	2.166667	1.366667	2.722222
Total
Count	12	12	12
Sum	66	82	86
Average	5.5	6.833333	7.166667
Variance	2.090909	2.69697	1.606061
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Time of day	0.44	1	0.44	0.19	0.6634	4.1709
Intensity	18.67	2	9.33	4.06	0.0276	3.3158
Time of day x Intensity	0.89	2	0.44	0.19	0.8253	3.3158
Error	69	30	2.3
Total	89	35