A researcher wants to determine if ACT scores are significantly different for st
ID: 3265432 • Letter: A
Question
A researcher wants to determine if ACT scores are significantly different for students taking two different ACT prep courses or no course: course 1 was designed by a local teacher, course 2 was prepared by ACT, the third group had no course. Gender 1=female, 2=male.
Subject
Gender
Course
Practice
December ACT
April ACT
1
1
1
10
18
17
2
1
1
12
19
20
3
1
1
10
14
15
4
1
1
12
16
17
5
2
1
11
18
19
6
2
1
12
17
20
7
2
1
10
15
21
8
2
1
12
16
19
9
1
2
8
12
17
10
1
2
10
18
19
11
1
2
10
16
15
12
1
2
8
18
17
13
2
2
8
12
17
14
2
2
10
18
20
15
2
2
10
16
17
16
2
2
8
17
15
17
1
3
12
16
17
18
1
3
16
19
21
19
1
3
14
16
19
20
1
3
12
16
19
21
2
3
12
16
17
22
2
3
16
19
20
23
2
3
14
18
19
24
2
3
12
16
15
1. What is the mean of the December ACT scores for all males?
2. What is the mean of the April ACT scores for the total sample?
3. What is the value of Mauchly’s W statistic? (Enter the value to three decimal places: #.###) _____
4. What conclusion regarding the assumption of sphericity can be made?
Subject
Gender
Course
Practice
December ACT
April ACT
1
1
1
10
18
17
2
1
1
12
19
20
3
1
1
10
14
15
4
1
1
12
16
17
5
2
1
11
18
19
6
2
1
12
17
20
7
2
1
10
15
21
8
2
1
12
16
19
9
1
2
8
12
17
10
1
2
10
18
19
11
1
2
10
16
15
12
1
2
8
18
17
13
2
2
8
12
17
14
2
2
10
18
20
15
2
2
10
16
17
16
2
2
8
17
15
17
1
3
12
16
17
18
1
3
16
19
21
19
1
3
14
16
19
20
1
3
12
16
19
21
2
3
12
16
17
22
2
3
16
19
20
23
2
3
14
18
19
24
2
3
12
16
15
Explanation / Answer
Answer:
SPSS used.
1. What is the mean of the December ACT scores for all males?
Mean=16.5
2. What is the mean of the April ACT scores for the total sample?
Mean= 18.0
3. What is the value of Mauchly’s W statistic? (Enter the value to three decimal places: #.###) _____
Mauchly’s W statistic = 0.901
Mauchly's Test of Sphericitya
Measure: MEASURE_1
Within Subjects Effect
Mauchly's W
Approx. Chi-Square
df
Sig.
Epsilonb
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
factor1
.901
1.773
2
.412
.910
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. Design: Intercept + Gender + Course + Gender * Course
Within Subjects Design: factor1
b. 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.
4. What conclusion regarding the assumption of sphericity can be made?
Calculated chi square=1.773, P=0.412 which is > 0.05 level. We conclude that assumption of sphericity is not violated.
Descriptive Statistics
Gender
Course
Mean
Std. Deviation
N
Practice
Female
Local
11.0000
1.15470
4
ACT
9.0000
1.15470
4
No course
13.5000
1.91485
4
Total
11.1667
2.32900
12
Male
Local
11.2500
.95743
4
ACT
9.0000
1.15470
4
No course
13.5000
1.91485
4
Total
11.2500
2.30119
12
Total
Local
11.1250
.99103
8
ACT
9.0000
1.06904
8
No course
13.5000
1.77281
8
Total
11.2083
2.26465
24
DecemberACT
Female
Local
16.7500
2.21736
4
ACT
16.0000
2.82843
4
No course
16.7500
1.50000
4
Total
16.5000
2.06706
12
Male
Local
16.5000
1.29099
4
ACT
15.7500
2.62996
4
No course
17.2500
1.50000
4
Total
16.5000
1.83402
12
Total
Local
16.6250
1.68502
8
ACT
15.8750
2.53194
8
No course
17.0000
1.41421
8
Total
16.5000
1.91107
24
AprilACT
Female
Local
17.2500
2.06155
4
ACT
17.0000
1.63299
4
No course
19.0000
1.63299
4
Total
17.7500
1.86474
12
Male
Local
19.7500
.95743
4
ACT
17.2500
2.06155
4
No course
17.7500
2.21736
4
Total
18.2500
2.00567
12
Total
Local
18.5000
2.00000
8
ACT
17.1250
1.72689
8
No course
18.3750
1.92261
8
Total
18.0000
1.91107
24
Tests of Within-Subjects Effects
Measure: MEASURE_1
Source
Type III Sum of Squares
df
Mean Square
F
Sig.
factor1
Sphericity Assumed
611.028
2
305.514
198.171
.000
Greenhouse-Geisser
611.028
1.820
335.774
198.171
.000
Huynh-Feldt
611.028
2.000
305.514
198.171
.000
Lower-bound
611.028
1.000
611.028
198.171
.000
factor1 * Gender
Sphericity Assumed
.861
2
.431
.279
.758
Greenhouse-Geisser
.861
1.820
.473
.279
.738
Huynh-Feldt
.861
2.000
.431
.279
.758
Lower-bound
.861
1.000
.861
.279
.604
factor1 * Course
Sphericity Assumed
31.389
4
7.847
5.090
.002
Greenhouse-Geisser
31.389
3.640
8.624
5.090
.003
Huynh-Feldt
31.389
4.000
7.847
5.090
.002
Lower-bound
31.389
2.000
15.694
5.090
.018
factor1 * Gender * Course
Sphericity Assumed
11.222
4
2.806
1.820
.146
Greenhouse-Geisser
11.222
3.640
3.083
1.820
.154
Huynh-Feldt
11.222
4.000
2.806
1.820
.146
Lower-bound
11.222
2.000
5.611
1.820
.191
Error(factor1)
Sphericity Assumed
55.500
36
1.542
Greenhouse-Geisser
55.500
32.756
1.694
Huynh-Feldt
55.500
36.000
1.542
Lower-bound
55.500
18.000
3.083
Mauchly's Test of Sphericitya
Measure: MEASURE_1
Within Subjects Effect
Mauchly's W
Approx. Chi-Square
df
Sig.
Epsilonb
Greenhouse-Geisser
Huynh-Feldt
Lower-bound
factor1
.901
1.773
2
.412
.910
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. Design: Intercept + Gender + Course + Gender * Course
Within Subjects Design: factor1
b. 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.
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