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 experiment wise alpha equal to 0.05.) 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.

Explanation / Answer

Solution:

a. F-table

Main effect for the time of day

Since the p-value of factor 1 (in excel output) is greater than 0.05 significance level, we retain the null hypothesis.

Main effect of intensity

Since the p-value of factor 2 (in excel output) is less than 0.01 significance level, we reject the null hypothesis.

Interaction effect

Since the p-value of interaction (in excel output) is greater than 0.05 significance level, we retain the null hypothesis.

b. The critical value is 2.88 for each pairwise comparison. (From excel output).

Two factor ANOVA Factor 2 Means: Column 1 Column 2 Column 3 Row 1 5.3 6.3 7.2 6.3 Factor 1 Row 2 5.5 7.2 7.2 6.6 5.4 6.8 7.2 6.4 6 replications per cell ANOVA table Source SS    df MS F    p-value Factor 1 1.00 1 1.000 0.45 .5075 Factor 2 20.06 2 10.028 4.51 .0193 Interaction 1.17 2 0.583 0.26 .7709 Error 66.67 30 2.222 Total 88.89 35 Post hoc analysis p-values for pairwise t-tests for Factor 2 Column 1 Column 2 Column 3 5.4 6.8 7.2 Column 1 5.4 Column 2 6.8 .0364 Column 3 7.2 .0074 .4988 Tukey simultaneous comparison t-values (d.f. = 30) Column 1 Column 2 Column 3 5.4 6.8 7.2 Column 1 5.4 Column 2 6.8 2.19 Column 3 7.2 2.88 0.68                critical values for experimentwise error rate: 0.05 2.47 0.01 3.15

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