Question

1.) 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	4
		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

(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

Using Minitab software, (Stat -> ANOVA -> General Linear Model), we get the following output :

Testing the significance of interaction between Light Intensity and Time of the day,

The value of test statistic= 0.21

and P-value = 0.813

Since P-value > 0.05, so we fail to reject H₀ at 5% level of significance and we can conclude that there is no significant interaction present between Light Intensity and Time of the day.

Testing the significance of Light Intensity,

The value of test statistic= 3.83

and P-value = 0.033

Since P-value < 0.05, so we reject H₀ at 5% level of significance and we can conclude that there is significant effect of light Intensity on mood rating.

Testing the significance of Time of the day,

The value of test statistic= 0.18

and P-value = 0.678

Since P-value > 0.05, so we fail reject H₀ at 5% level of significance and we can conclude that there is no significant effect of Time of the day on mood rating.

b)