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.)

Time of day SS df MS F

Intesity SS df MS F

Time of day * Intesity SS df MS F

Error SS df MS

Total SS df

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 8 8 Night 5 6 9 8 8 7 6 7 6 7 5 8 3 9 7 3 8 6

Explanation / Answer

a. The hypotheses for main factor A, Time of the day, main factor B, Intensity of day, and interaction factor is as follows:

H0: mu morning=mu night=0 (there is no difference in mean mood score during two time of the day)

H1: there is difference in mean mood score.

H0: mu low=mu medium=mu high (there is no difference in mean mood score during three type of light intensity)

H1:atleast one mean mood score is different from another.

H0: there is no interaction between the factors A and B.

H1: there is interaction between the factors.

Compute F test statistic.

Enter the given data in MS Excel-Data-Data Analysis-Anova: Two factor with Replication-enter input range A1:D13-Enter 6 in Rows per sample-select F4 as Output range-Click Ok. The following table demonstrate the output.

The p value for Time of day is 0.75, Intensity, and Time of day*Intensity are 0.75, 0.02, and 0.78 respectively. Per rule, reject H0, if p value is less than assumed level of significance, alpha=0.05. Thus, retain H0 for factor-Time of day, and interaction-Time of day*Intensity, and reject H0 for factor Intensity. Therefore, the main effect due to factor B, that is Intensity is significant.

Source of variation SS df MS F Time of day 0.25 1 0.25 0.10 Intensity 20.72 2 10.36 4.27 Time of day*Intensity 1.17 2 0.58 0.24 Error 72.83 30 2.43 Total 94.97 35

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