Computer Assignment 4
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Computer Assignment 4
Computer Assignment 4
Problem 1
Let's assume a professor in physical education conducts an experiment to compare the effects on nighttime sleep of different amounts of exercise and the time of day when the exercise is done. The experiment uses a fixed effects 3x2 factorial design with independent groups. There are three levels of exercise (light, moderate, heavy) and two times of day (morning and evening).Thirty-six college students in good physical conditions are randomly assigned to the six cells such that there are six subjects per cell. The subjects who do heavy exercise jog for 3 miles, the subjects who do moderate exercise jog for 1 mile and those in the light exercise group jog for only ¼ mile. Morning exercise is done at 7:30 am while evening exercise is done at 7:00 PM. Each subject exercises once and the number of hours slept that night is recorded.
Light
Moderate
Heavy
Morning
6.5
7.4
8
7.3
6.8
7.7
6.6
6.7
7.1
7.4
7.3
7.6
7.2
7.6
6.6
6.8
7.4
7.2
Evening
7.1
7.4
8.2
7.9
8.1
8.5
8.2
8.2
9.5
7.7
8
8.7
7.5
7.6
9.6
7.6
8
9.4
Solution
The professor in physical education conducts an experiment for identifying the night time sleep of dissimilar numbers of exercise and the day time. He use three level of exercise such as light, moderate and heavy and noticed an observation on that exercise (Tabachnick,et.al, 2001)..
ANOVA table will help the professor to analyze the different level of measures and their effectiveness. This ANOVA table is obtaining by using the SPSS table.
Analyze-Generalize Linear Models-Univariate
Hence, the values has based on different levels, so two way ANOVA is best for analyzing the effects at different levels (Wilcox,et.al,1986).
Tests of Between-Subjects Effects
Dependent Variable: Values
Source
Type III Sum of Squares
df
Mean Square
F
Sig.
Corrected Model
15.466a
5
3.093
16.640
.000
Intercept
2122.138
1
2122.138
11416.163
.000
Exercise
15.466
5
3.093
16.640
.000
Error
5.577
30
.186
Total
2143.180
36
Corrected Total
21.042
35
a. R Squared = .735 (Adjusted R Squared = .691)
L.M
Low - Morning
M.M
Moderate-Morning
H.M
High - Morning
L.E
Low-Evening
M.E
Moderate-Evening
H.E
High-Evening
Multiple Comparisons
Dependent Variable: Values
(I) Exercise
(J) Exercise
Mean Difference (I-J)
Std. Error
Sig.
95% Confidence Interval
Lower Bound
Upper Bound
LSD
L.M
L.E
-.700*
.2489
.009
-1.208
-.192
M.M
-.233
.2489
.356
-.742
.275
M.E
-.917*
.2489
.001
-1.425
-.408
H.M
-.400
.2489
.119
-.908
.108
H.E
-2.017*
.2489
.000
-2.525
-1.508
L.E
L.M
.700*
.2489
.009
.192
1.208
M.M
.467
.2489
.071
-.042
.975
M.E
-.217
.2489
.391
-.725
.292
H.M
.300
.2489
.238
-.208
.808
H.E
-1.317*
.2489
.000
-1.825
-.808
M.M
L.M
.233
.2489
.356
-.275
.742
L.E
-.467
.2489
.071
-.975
.042
M.E
-.683*
.2489
.010
-1.192
-.175
H.M
-.167
.2489
.508
-.675
.342
H.E
-1.783*
.2489
.000
-2.292
-1.275
M.E
L.M
.917*
.2489
.001
.408
1.425
L.E
.217
.2489
.391
-.292
.725
M.M
.683*
.2489
.010
.175
1.192
H.M
.517*
.2489
.047
.008
1.025
H.E
-1.100*
.2489
.000
-1.608
-.592
H.M
L.M
.400
.2489
.119
-.108
.908
L.E
-.300
.2489
.238
-.808
.208
M.M
.167
.2489
.508
-.342
.675
M.E
-.517*
.2489
.047
-1.025
-.008
H.E
-1.617*
.2489
.000
-2.125
-1.108
H.E
L.M
2.017*
.2489
.000
1.508
2.525
L.E
1.317*
.2489
.000
.808
1.825
M.M
1.783*
.2489
.000
1.275
2.292
M.E
1.100*
.2489
.000
.592
1.608
H.M
1.617*
.2489
.000
1.108
2.125
Based on observed means.
The error term is Mean Square (Error) = .186.
*. The mean difference is significant at the .05 level.
Tables of Exercise
Exercise
N
Subset
1
2
3
4
Student-Newman-Keulsa,b
L.M
6
6.967
M.M
6
7.200
7.200
H.M
6
7.367
7.367
7.367
L.E
6
7.667
7.667
M.E
6
7.883
H.E
6
8.983
Sig.
.258
.164
.112
1.000
Means for groups in homogeneous subsets are displayed.
Based on observed means.
The error term is Mean Square (Error) = .186.
a. Uses Harmonic Mean Sample Size = 6.000.
b. Alpha = .05.
1.What number above is the average variance in each group? 0.185889
2.What number above is the denominator for each F ratio? _____16.640___________
3.What number above is the variability of the cell means around the grand mean after you have subtracted out the variance due to the main effects? _____4.5848______
4.What number above is the variance among the intensity of exercise main effect means? __2122.138______
5.How many df are in each of the 6 groups 5
Conclusion
The intercept f value is extremely higher whereas the exercise and the corrected model are same. The f value defines the significance level and the evening exercise has higher value rather than the morning values (Freund & Littell,1981).
Problem-22
A clinical psychologist is interested in the effect that anxiety has on the ability of individuals to learn new material. She is also interested in whether the effect of anxiety depends on the difficulty of the new material. An experiment is conducted in which there are three levels of anxiety (high, medium, low) and three levels of difficulty (high, medium, and low) ...