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

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

Anova: Two-Factor Wit+A27+A1:C31+A1:C+A1:G30
SUMMARY	Low	Medium	High	Total
morning
Count	6	6	6	18
Sum	33	39	43	115
Average	5.5	6.5	7.166666667	6.388888889
Variance	1.1	3.5	2.166666667	2.486928105
night
Count	6	6	6	18
Sum	33	43	43	119
Average	5.5	7.166666667	7.166666667	6.611111111
Variance	3.5	2.166666667	1.366666667	2.722222222
Total
Count	12	12	12
Sum	66	82	86
Average	5.5	6.833333333	7.166666667
Variance	2.090909091	2.696969697	1.606060606
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
time of day	0.444444444	1	0.444444444	0.193236715	0.663386732	4.170876786
intensity	18.66666667	2	9.333333333	4.057971014	0.027556176	3.315829501
time of day*intensity	0.888888889	2	0.444444444	0.193236715	0.825304705	3.315829501
Within	69	30	2.3
Total	89	35

if p-value < 0.05

we reject the null hypothesis

hence

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