Seasonal affective disorder (SAD) is a type of depression during seasons with le
ID: 3357079 • Letter: S
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.
Light Intensity Low Medium High Morning 5 Time of Day Night 6 9 (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 MS Time of day Intensity Time of day x Intensity TotalExplanation / Answer
Solution:
Part a
Completed F table is given as below:
Table is calculated by using excel.
Analysis of Variance for Mood Scale
Source DF SS MS F P
Day time 1 1.00 1.00 0.43 0.518
Light In 2 19.39 9.69 4.15 0.026
Interaction 2 0.50 0.25 0.11 0.899
Error 30 70.00 2.33
Total 35 90.89
From the above table, the p-value for the variable day time is given as 0.518 which is greater than the level of significance or alpha value 0.05, so we do not reject the null hypothesis that the factor day time is not statistically significant. The p-value for the variable light intensity is given as 0.026 which is less than the level of signficanc3e or alpha value 0.05, so we reject the null hypothesis that the light intensity is not statistically significant. This concludes that the light intensity is statistically significant. The p-value for the interaction between the day time and light intensity is given as 0.899 which is greater than the 5% level of significance, so we do not reject the null hypothesis that the interaction between the two variables day time and light intensity are not statistically significant. There is no any significant effect occurs due to interaction of the day time and light intensity.
Part b
Now, we have to find the critical value for Tukey’s HSD by using the table for critical values for HSD.
We are given, k = number of treatments = 2
And df for error term = 30
So, critical value = 2.89
Required answer: 2.89
The pairwise comparisons by using Tukey HSD is given as below:
Multiple Comparisons
Mood Scale
Tukey HSD
(I) Light Intensity
(J) Light Intensity
Mean Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
Low
Medium
-1.4167
.62361
.076
-2.9540
.1207
High
-1.6667*
.62361
.031
-3.2040
-.1293
Medium
Low
1.4167
.62361
.076
-.1207
2.9540
High
-.2500
.62361
.915
-1.7874
1.2874
High
Low
1.6667*
.62361
.031
.1293
3.2040
Medium
.2500
.62361
.915
-1.2874
1.7874
Based on observed means.
The error term is Mean Square(Error) = 2.333.
*. The mean difference is significant at the 0.05 level.
Only pair low to high is statistically significant. All other pairs are not statistically significant.
Multiple Comparisons
Mood Scale
Tukey HSD
(I) Light Intensity
(J) Light Intensity
Mean Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
Low
Medium
-1.4167
.62361
.076
-2.9540
.1207
High
-1.6667*
.62361
.031
-3.2040
-.1293
Medium
Low
1.4167
.62361
.076
-.1207
2.9540
High
-.2500
.62361
.915
-1.7874
1.2874
High
Low
1.6667*
.62361
.031
.1293
3.2040
Medium
.2500
.62361
.915
-1.2874
1.7874
Based on observed means.
The error term is Mean Square(Error) = 2.333.
*. The mean difference is significant at the 0.05 level.
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