Seasonal affective disorder (SAD) is a type of depression during seasons with le

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.

(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.)

(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.

   Light Intensity Low Medium High Time of
Day Morning 5 4 6 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 6 5 8 4 8 7 3 8 6

Explanation / Answer

Solution:

a. F-table

Since p-value of time of day and time of day x Intensity is greater than 0.05, we fail to reject the null hypothesis and p-value of intensity is less than 0.05, we reject the null hypothesis.

b.

c. The variable Intensity is statistically significant. Since the pairwise p-values are greater than 0.01, therefore none of the variable is statistically significant.

Two factor ANOVA Factor 2 Means: Column 1 Column 2 Column 3 Morning 5.5 6.3 7.0 6.3 Factor 1 Row 2 5.3 7.0 7.2 6.5 5.4 6.7 7.1 6.4 6 replications per cell ANOVA table Source SS    df MS F    p-value Factor 1 0.44 1 0.444 0.19 .6634 Factor 2 18.06 2 9.028 3.93 .0306 Interaction 1.06 2 0.528 0.23 .7963 Error 69.00 30 2.300 Total 88.56 35 Post hoc analysis p-values for pairwise t-tests for Factor 2 Column 1 Column 2 Column 3 5.4 6.7 7.1 Column 1 5.4 Column 2 6.7 .0525 Column 3 7.1 .0115 .5061 Tukey simultaneous comparison t-values (d.f. = 30) Column 1 Column 2 Column 3 5.4 6.7 7.1 Column 1 5.4 Column 2 6.7 2.02 Column 3 7.1 2.69 0.67                critical values for experimentwise error rate: 0.05 2.47 0.01 3.15

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