Answer To: 1. A chiropractor wants to help her patients who suffer from chronic back pain reduce their pain...
Pooja answered on Apr 25 2021
1. A chiropractor wants to help her patients who suffer from chronic back pain reduce their pain levels. To do this, the doctor investigates whether different chiropractic treatments are more effective at reducing pain levels over time. Thirty people volunteer to participate in the experiment and are randomly assigned to one of three treatment groups. One group receives a massage treatment for their back pain (treatment=1); a second group participates in an acupuncture program (treatment=2), and the third group participates in an online mindfulness program (treatment=3). Each program lasts for six weeks. Over this six-week period, back pain is measured at three time points, with higher scores representing more pain: at the beginning of the program (time 1), after three-weeks (time 2), and at the end of the program (time 3). The data for this study are presented below. Use an alpha of .05 to answer the questions below.
Person
Treatment
Time 1
Time 2
Time 3
Person
Treatment
Time 1
Time 2
Time 3
1
1
85
85
88
16
2
84
86
89
2
1
90
92
93
17
2
103
109
90
3
1
97
97
94
18
2
92
96
101
4
1
80
82
83
19
2
97
98
100
5
1
91
92
91
20
2
102
104
103
6
1
83
83
84
21
3
93
98
110
7
1
87
88
90
22
3
98
104
112
8
1
92
94
95
23
3
98
105
99
9
1
97
99
96
24
3
87
132
120
10
1
100
97
100
25
3
94
110
116
11
2
86
86
84
26
3
95
126
143
12
2
93
103
104
27
3
100
126
140
13
2
90
92
93
28
3
103
124
140
14
2
95
96
100
29
3
94
135
130
15
2
89
96
95
30
3
99
111
150
a) What is the most appropriate statistical analysis we discussed this semester to analyze these data?
Ans : Repeated measure Anova, MANOVA
b) Identify the between-subject and within-subject factors.
Ans : Within subject factor is Time
Within subjects effect is a measure of how much the back pain scores in an individual vary over
Time.
Between subject factor is Treatment
which examine the difference between the individuals. i.e comparing the back pain scores between
the subjects with various treatment.
c) Do we meet the assumption of Sphericity? What information did you use to come to this conclusion?
Ans : To test the assumption of sphericity we will use the Mauchly’s test of sphericity with repeated measure ANOVA. if value of Mauchly's Test of Sphericity is statistically significant (p < .05), we can reject the null hypothesis and accept the alternative hypothesis that the variances of the differences are not equal it means sphericity assumption has been violated. If the sphericity is violated then we can use Greenhouse-Geisser, Huynh-Feldt correction.
Mauchly's Test of Sphericity(b)
Measure: MEASURE_1
Within Subjects Effect
Mauchly's W
Approx. Chi-Square
df
Sig.
Epsilon(a)
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
time
.968
.844
2
.656
.969
1.000
.500
Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed dependent variables is proportional to an identity matrix.
a May be used to adjust the degrees of freedom for the averaged tests of significance. Corrected tests are displayed in the Tests of Within-Subjects Effects table.
b Design: Intercept+Treatment
Within Subjects Design: time
From the above results we found that significance value is not less than 0.05.(p=0.656) So we accept the null hypothesis & assume that variance of difference are equal. So it means assumption is not violated & meeting the criteria.
d) Were the three treatment programs equally effective in reducing back pain? What information did you use to come to this conclusion?
Ans :
Table 1
Table 2
Tests of Within-Subjects Effects
Measure: treatment
Source
Type III Sum of Squares
df
Mean Square
F
Sig.
Partial Eta Squared
time
Sphericity Assumed
2,066.600
2
1,033.300
23.543
0.000
0.466
Greenhouse-Geisser
2,066.600
1.938
1,066.307
23.543
0.000
0.466
Huynh-Feldt
2,066.600
2.000
1,033.300
23.543
0.000
0.466
Lower-bound
2,066.600
1.000
2,066.600
23.543
0.000
0.466
time * Treatment
Sphericity Assumed
2,723.333
4
680.833
15.512
0.000
0.535
Greenhouse-Geisser
2,723.333
3.876
702.581
15.512
0.000
0.535
Huynh-Feldt
2,723.333
4.000
680.833
15.512
0.000
0.535
Lower-bound
2,723.333
2.000
1,361.667
15.512
0.000
0.535
Error(time)
Sphericity Assumed
2,370.067
54
43.890
Greenhouse-Geisser
2,370.067
52.328
45.292
Huynh-Feldt
2,370.067
54.000
43.890
Lower-bound
2,370.067
27.000
87.780
Table 3
Tests of Between-Subjects Effects
Measure: MEASURE_1
Transformed Variable: Average
Source
Type III Sum of Squares
df
Mean Square
F
Sig.
Partial Eta Squared
Intercept
894608.100
1
894608.100
5802.399
.000
.995
Treatment
8326.067
2
4163.033
27.001
.000
.667
Error
4162.833
27
154.179
Estimates
Measure: MEASURE_1
Treatment
Mean
Std. Error
95% Confidence Interval
Lower Bound
Upper Bound
Treatment 1
90.833
2.267
86.182
95.485
Treatment 2
95.200
2.267
90.548
99.852
Treatment 3
113.067
2.267
108.415
117.718
Table 4
A repeated-measures ANOVA determined that mean reducing pain scores differed significantly across the time points (F = 23.54, p = .000). (table 2)
Treatment is having significant in the reducing the back pain. (F=27.001, p= 0.000) partial η2 =.667
A post hoc pairwise comparison using the Tukey HSD showed which treatment is more effective among the three treatments.
Pair Treatment 1-treatment 2 there is no...