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.)

Light Intensity Low Medium High Time of Morning 5 5 7 Day 6 6 8 4 4 6 7 7 9 5 9 5 5 8 8 Night 5 6 9 8 8 7 6 7 6 7 5 8 4 9 7 3 8 6

Explanation / Answer

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).

Here row variable is time of day and column variable is light intensity.

Here we have to test the hypothesis that,

H0 :Time of day is insignificant.

H1 : Time of day is significant

H0 : Light intensity is insignificant.

H1 : Light intensity is significant.

H0 : Intersection is insignificant.

H1 : Intersection is significant.

Assume alpha = level of significance = 5% = 0.05

This is two way ANOVA with interaction.

We can do two way ANOVA with interaction in MINITAB.

steps :

ENTER data into MINITAB sheet --> STAT --> ANOVA --> Two way ANOVA --> Response : select data column --> Row factor : time of day --> Column factor : light intensity --> DOn't click on fit additive model --> ok

Two-way ANOVA: observation versus time of day, light intensity

Analysis of Variance for observat
Source DF SS MS F P
time of 1 0.69 0.69 0.30 0.586
light in 2 20.72 10.36 4.52 0.019
Interaction 2 0.72 0.36 0.16 0.855
Error 30 68.83 2.29
Total 35 90.97

Now we can see that time of day is insignificant variable and light intensity is significant variable.

Also interaction is insignificant variable.

(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test.

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