In a longitudinal study of attitude toward statistics, a doctoral student surveyed 10 doctoral
students at four times during their program: (a) before taking any statistics courses; (b) after
having taken one course; (c) after all required statistics courses; and (d) one semester after
completing their preliminary examination. In each instance, alternate forms of the Attitude
Towards Statistics instrument were used. The data were:
1. Analyze the data using an alpha of .05 in SPSS (Free trial of SPSS here: http://www-
01.ibm.com/software/analytics/spss/products/statistics/downloads.html)
2. Writing the result in APA format.
Solution
SPSS out put
GLM v1 v2 v3 v4
/WSFACTOR=factor1 4 Polynomial
/METHOD=SSTYPE(3)
/EMMEANS=TABLES(factor1) COMPARE ADJ(BONFERRONI)
/PRINT=DESCRIPTIVE
/CRITERIA=ALPHA(.05)
/WSDESIGN=factor1.
Descriptive Statistics
Mean
Std. Deviation
N
v1
40.50
11.008
10
v2
42.40
11.806
10
v3
43.00
11.126
10
v4
36.80
10.390
10
Multivariate Testsa
Effect
Value
F
Hypothesis df
Error df
Sig.
factor1
Pillai\'s Trace
.768
7.725b
3.000
7.000
.013
Wilks\' Lambda
.232
7.725b
3.000
7.000
.013
Hotelling\'s Trace
3.311
7.725b
3.000
7.000
.013
Roy\'s Largest Root
3.311
7.725b
3.000
7.000
.013
a. Design: Intercept
Within Subjects Design: factor1
b. Exact statistic
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
.509
5.209
5
.394
.688
.896
.333
Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed
dependent variables is proportional to an identity matrix.
a. Design: Intercept
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.
Tests of Within-Subjects Effects
Measure: MEASURE_1
Source
Type III Sum of Squares
df
Mean Square
F
Sig.
factor1
Sphericity Assumed
234.275
3
78.092
15.916
.000
Greenhouse-Geisser
234.275
2.064
113.520
15.916
.000
Huynh-Feldt
234.275
2.687
87.190
15.916
.000
Lower-bound
234.275
1.000
234.275
15.916
.003
Error(factor1)
Sphericity Assumed
132.475
27
4.906
Greenhouse-Geisser
132.475
18.574
7.132
Huynh-Feldt
132.475
24.182
5.478
Lower-bound
132.475
9.000
14.719
Tests of Within-Subjects Contrasts
Measure: MEASURE_1
Source
factor1
Type III Sum of Squares
df
Mean Square
F
Sig.
factor1
Linear
55.125
1
55.125
20.066
.002
Quadratic
164.025
1
164.025
18.401
.002
Cubic
15.125
1
15.125
4.946
.053
Error(factor1)
Linear
24.725
9
2.747
Quadratic
80.225
9
8.914
Cubic
27.525
9
3.058
Tests of Between-Subjects Effects
Measure: MEASURE_1
Transformed Variable: Average
Source
Type III Sum of Squares
df
Mean Square
F
Sig.
Intercept
66178.225
1
66178.225
138.576
.000
Error
4298.025
9
477.558
Estimated Marginal Means
factor1
Estimates
Measure: MEASURE_1
factor1
Mean
Std. Error
95% Confidence Interval
Lower Bound
Upper Bound
1
40.500
3.481
32.626
48..
In a longitudinal study of attitude toward statistics, a doctoral st.pdf
1. In a longitudinal study of attitude toward statistics, a doctoral student surveyed 10 doctoral
students at four times during their program: (a) before taking any statistics courses; (b) after
having taken one course; (c) after all required statistics courses; and (d) one semester after
completing their preliminary examination. In each instance, alternate forms of the Attitude
Towards Statistics instrument were used. The data were:
1. Analyze the data using an alpha of .05 in SPSS (Free trial of SPSS here: http://www-
01.ibm.com/software/analytics/spss/products/statistics/downloads.html)
2. Writing the result in APA format.
Solution
SPSS out put
GLM v1 v2 v3 v4
/WSFACTOR=factor1 4 Polynomial
/METHOD=SSTYPE(3)
/EMMEANS=TABLES(factor1) COMPARE ADJ(BONFERRONI)
/PRINT=DESCRIPTIVE
/CRITERIA=ALPHA(.05)
/WSDESIGN=factor1.
Descriptive Statistics
Mean
Std. Deviation
N
v1
40.50
11.008
10
v2
42.40
11.806
10
v3
43.00
11.126
10
3. a. Design: Intercept
Within Subjects Design: factor1
b. Exact statistic
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
.509
5.209
5
.394
.688
.896
.333
Tests the null hypothesis that the error covariance matrix of the orthonormalized transformed
dependent variables is proportional to an identity matrix.
a. Design: Intercept
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.
Tests of Within-Subjects Effects
Measure: MEASURE_1
Source
Type III Sum of Squares
df
Mean Square
F
Sig.
5. 24.182
5.478
Lower-bound
132.475
9.000
14.719
Tests of Within-Subjects Contrasts
Measure: MEASURE_1
Source
factor1
Type III Sum of Squares
df
Mean Square
F
Sig.
factor1
Linear
55.125
1
55.125
20.066
.002
Quadratic
164.025
1
164.025
18.401
.002
Cubic
15.125
1
15.125
4.946
.053
Error(factor1)
Linear
10. -10.237
-2.163
Based on estimated marginal means
*. The mean difference is significant at the .05 level.
b. Adjustment for multiple comparisons: Bonferroni.
Multivariate Tests
Value
F
Hypothesis df
Error df
Sig.
Pillai's trace
.768
7.725a
3.000
7.000
.013
Wilks' lambda
.232
7.725a
3.000
7.000
.013
Hotelling's trace
3.311
7.725a
3.000
7.000
.013
Roy's largest root
3.311
7.725a
3.000
7.000
.013
Each F tests the multivariate effect of factor1. These tests are based on the linearly independent
11. pairwise comparisons among the estimated marginal means.
a. Exact statistic
Report
A one-way within subjects (or repeated measures) ANOVA was conducted to compare the
attitude towards statistics. There was a significant effect of the course, Wilks
Descriptive Statistics
Mean
Std. Deviation
N
v1
40.50
11.008
10
v2
42.40
11.806
10
v3
43.00
11.126
10
v4
36.80
10.390
10
