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
		5	6	8
		4	4	6
		7	7	9
		5	8	5
		6	8	8
	Night	4	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

I have worked on this for three days, can't get it. Please help!

Answer 1

Load the data into Excel.

Go to Data> Data Analysis.

Go to ANOVA: Two Factor With replication.

Select the data into the Input Range.

Select the replications as 5.

Click OK.

The output is as follows:

SUMMARY	low	medium	high	Total
Count	6	6	6	18
Sum	32	38	43	113
Average	5.333333	6.333333	7.166667	6.277778
Variance	1.066667	2.666667	2.166667	2.330065
night
Count	6	6	6	18
Sum	32	43	43	118
Average	5.333333	7.166667	7.166667	6.555556
Variance	3.866667	2.166667	1.366667	2.96732
Total
Count	12	12	12
Sum	64	81	86
Average	5.333333	6.75	7.166667
Variance	2.242424	2.386364	1.606061
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	0.694444	1	0.694444	0.313283	0.579828	4.170877
Columns	22.16667	2	11.08333	5	0.013363	3.31583
Interaction	1.388889	2	0.694444	0.313283	0.733406	3.31583
Within	66.5	30	2.216667
Total	90.75	35

a)

ANOVA
Source of Variation	SS	df	MS	F
time of day	0.69	1.00	0.69	0.31
intensity	22.17	2.00	11.08	5.00
time of day*intensity	1.39	2.00	0.69	0.31
error	66.50	30.00	2.22
Total	90.75	35.00

from above only intensity is significant; therefore reject hypothesis for intensity but fail to reject fo time of day as well for interaction.

Please do the comment for any doubt or clarification. Please upvote if this helps you out. Thank You!