Seasonal affective disorder (SAD) is a type of depression during seasons with le
ID: 3361224 • 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 Time ofDay Morning 5 5 7 6 6 8 4 4 6 6 7 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
(a) The F-table
In our data there are 3 different intensities of light low, medium and high 2 different time of day Morning and Night with 5 different temperatures.
Hypotheses:
There are three sets of hypothesis tests for the Two-Way ANOVA
1. H0: The means of each row (time of day) are equal
H1: The mean of at least one row (time of day) is different
2. H0: The means of each column (intensity) are equal
H2: The mean of at least one column (intensity) is different
3. H0: There is no interaction between the row (time of day) and column (intensity)
H3: There is interaction between the row (time of day) and column (intensity)
Source of
SS
df
MS
F
Variation
Time of day
0.6944
1
0.6944
0.3117
Intensity
20.7222
2
10.3611
4.6508
Time of day x Intensity
0.7222
2
0.3611
0.162
Error
66.8333
30
2.2277
Total
88.9722
35
(b) Tukey's HSD to analyze the significant main effect
Pairwise Comparisons:
Pairwise Comparisons
Dependent Variable: Intensity
(I) LightIntensitylevel
(J) LightIntensitylevel
Mean Difference (I-J)
Std. Error
Sig.b
95% Confidence Interval for Differenceb
Lower Bound
Upper Bound
High
Low
1.750*
.609
.022
.205
3.295
Medium
.333
.609
1.000
-1.212
1.878
Low
High
-1.750*
.609
.022
-3.295
-.205
Medium
-1.417
.609
.081
-2.962
.128
Medium
High
-.333
.609
1.000
-1.878
1.212
Low
1.417
.609
.081
-.128
2.962
Based on estimated marginal means
*. The mean difference is significant at the .05 level.
b. Adjustment for multiple comparisons: Bonferroni.
Tukeys HSD:
Intensity
Tukey Ba,b
LightIntensitylevel
N
Subset
1
2
Low
12
5.42
Medium
12
6.83
High
12
7.17
Means for groups in homogeneous subsets are displayed.
Based on observed means.
The error term is Mean Square(Error) = 2.228.
a. Uses Harmonic Mean Sample Size = 12.000.
b. Alpha = .05.
) Summarization the results for this test::
The conclusion based on below results
ANOVA
Source of Variation
SS
df
MS
F
P-value
F crit
Sample
0.694444
1
0.694444
0.311721
0.58077
4.170877
Columns
20.72222
2
10.36111
4.650873
0.017404
3.31583
Interaction
0.722222
2
0.361111
0.162095
0.8511
3.31583
Error
66.83333
30
2.227778
Total
88.97222
35
1. The p-value is > 0.05 for the time of day as well as F < F crit, so we fail to reject the null hypothesis.
That means, the means of each time of day are equal
2. The p-value is < 0.05 for intensity as well as F > F crit, so we reject the null hypothesis.
That means, the mean of at least one intensity is different.
3. The p-value is > 0.05 for interaction between the time of day and intensity as well as F < F crit, so we fail to reject the null hypothesis.
That means, There is no interaction between the row (time of day) and column (intensity)
Source of
SS
df
MS
F
Variation
Time of day
0.6944
1
0.6944
0.3117
Intensity
20.7222
2
10.3611
4.6508
Time of day x Intensity
0.7222
2
0.3611
0.162
Error
66.8333
30
2.2277
Total
88.9722
35
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