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
		5	9	5
		6	7	8
	Night	5	6	9
		8	8	7
		6	6	6
		7	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

(b) Compute Tukey's HSD to analyze the significant main effect.

The critical value is ____ for each pairwise comparison.

(c) Summarize the results for this test using APA format.

Answer 1

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
time of day	0.11	1.00	0.11	0.05	0.82	4.17
intensity	15.72	2.00	7.86	3.68	0.04	3.32
Interaction	0.72	2.00	0.36	0.17	0.85	3.32
Within	64.00	30.00	2.13
Total	80.56	35.00

p value for time of day = 0.82 > 0.05,

effect not signifant

p value for intensity = 0.04 <0.05 , effects are significant

p value for interaction : 0.85 > 0.05, interaction not significant

..............

Level of significance	0.05
no. of treatments,k	3
DF error =N-k=	30
MSE	2.130
q-statistic value(α,k,N-k)	3.4900

critical value = q*√(MSE/n)

HSD =1.47 (critical value)

			confidence interval
population mean difference	critical value	lower limit	upper limit	result
µ1-µ2	-13.00	1.47	-14.47	-11.53	means are different
µ1-µ3	-19.00	1.47	-20.47	-17.53	means are different
µ2-µ3	-6.00	1.47	-7.47	-4.53	means are different

Please revert back in case of any doubt.

Please upvote. Thanks in advance.