Seasonal affective disorder (SAD) is a type of depression during seasons with le
ID: 3340202 • 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.
(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.
Light Intensity Low Medium High Time ofDay Morning 5 5 7 6 6 8 4 4 6 7 6 9 5 9 5 6 8 8 Night 5 6 9 8 8 7 6 7 6 7 5 8 4 9 7 3 8 6
Explanation / Answer
Result:
Two factor ANOVA
Factor 2
Means:
Low
Medium
High
Morning
5.5
6.3
7.2
6.3
Factor 1
Night
5.5
7.2
7.2
6.6
5.5
6.8
7.2
6.5
6
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Time
0.69
1
0.694
0.30
.5863
Light Intensity
18.06
2
9.028
3.93
.0304
Interaction
1.39
2
0.694
0.30
.7411
Error
68.83
30
2.294
Total
88.97
35
Post hoc analysis
Tukey simultaneous comparison t-values (d.f. = 30)
Low
Medium
High
5.5
6.8
7.2
Low
5.5
Medium
6.8
2.02
High
7.2
2.70
0.67
critical values for experimentwise error rate:
0.05
2.47
To test time effect, Calculated F=0.03, P=0.5863 which is > 0.05 level. Ho is not rejected. Time effect is not significant.
To test Light Intensity effect, Calculated F=3.93, P=0.0304 which is < 0.05 level. Ho is rejected. Light Intensity effect is significant.
To test interaction effect, Calculated F=0.03, P=0.7411 which is > 0.05 level. Ho is not rejected. Interaction effect is not significant..
Two factor ANOVA
Factor 2
Means:
Low
Medium
High
Morning
5.5
6.3
7.2
6.3
Factor 1
Night
5.5
7.2
7.2
6.6
5.5
6.8
7.2
6.5
6
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Time
0.69
1
0.694
0.30
.5863
Light Intensity
18.06
2
9.028
3.93
.0304
Interaction
1.39
2
0.694
0.30
.7411
Error
68.83
30
2.294
Total
88.97
35
Post hoc analysis
Tukey simultaneous comparison t-values (d.f. = 30)
Low
Medium
High
5.5
6.8
7.2
Low
5.5
Medium
6.8
2.02
High
7.2
2.70
0.67
critical values for experimentwise error rate:
0.05
2.47
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