Running head: SPSS CORRELATION & REGRESSION
SPSS Correlation & Regression Assignment
Deborah Davis
Liberty University
1
SPSS CORRELATION & REGRESSION
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The purpose of this document is to provide a response to the third SPSS assignment that
for the use and understanding of the correlation and regression in statistics. The research
scenario was given as a part of the assignment, and presumes leaders of colleges and universities
are seeking ways to develop and maintain online and blended programs (Szapkiw, 2014, p. 2).
This particular assignment required the use of SPSS to “choose the appropriate tests . . . run the
tests and analyze the data” (Szapkiw, 2014, p. 14).
Structure
In that there are two aspects to this assignment and seven sections to each of them, and it
is a small college paper, it will only use the first two levels of headings, and it will be separated
by assignment section within each aspect.
Research Question 1
Is there a statistically significant relationship between students’ total community score as
measured by the Classroom Community Scale (Rovai, 2002) and the total perceived learning
scores as measured by the Perceived CAP Learning Scale (Rovai et al., 2009) after controlling
for gender among students who are enrolled in the Introduction to Statistics course.
Null Hypothesis 1
There is no significant relationship between students’ total community score as measured
by the Classroom Community Scale (Rovai, 2002) and the total perceived learning scores as
measured by the Perceived CAP Learning Scale (Rovai et al., 2009) after controlling for gender
among students who are enrolled in the Introduction to Statistics course.
Alternative Hypothesis 1
There is a significant relationship between students’ total community score as measured
by the Classroom Community Scale (Rovai, 2002) and the total perceived learning scores as
SPSS CORRELATION & REGRESSION
3
measured by the Perceived CAP Learning Scale (Rovai et al., 2009) after controlling for gender
among students who are enrolled in the Introduction to Statistics course.
Continuous Variables
Students’ total community score as measured by the Classroom Community Scale (Rovai,
2002)
Students’ total perceived learning scores as measured by the Perceived CAP Learning
Scale (Rovai et al., 2009)
Test to be Used
Partial correlation was used to evaluate the null hypothesis that there is no significant
relationship between students’ total community sore as measured by the Classroom Community
Scale (Rovai, 2002) and the total perceived learning scores as measured by the Perceived CAP
Learning Scale (Rovai et al., 2009), while controlling for gender (N = 40). This was the most
appropriate analysis as it assists researchers in examining the strength and direction of the linear
relationship between two variables, while controlling for another variable (i.e. confounding
variable; a variable you suspect influences the other two variables; Warner, 2013). A bivariate
correlation is ruled out because the researcher is not interested in the relationship between only
two variables.
Assumptions
Preliminary analyses using a scatter plot were performed to ensure no violations of the
assumptions of linearity, bivariate normality, and homoscedasticity; assumptions were found
tenable.
1) Normality: This assumption assumes that the population distributions are normal. Check for
normality by creating histograms or by conducting normality tests, such as the Shapiro-Wilk and
SPSS CORRELATION & REGRESSION
4
Kolmogorov-Smirnov tests. On the histogram, normality is assumed when there is a
symmetrical, bell shaped curve. For the normality tests, non-significant results (a significance
level more than .05 indicate tenability of the assumption. That is, normality can be assumed.
Community sore as measured by the Classroom Community Scale (Rovai, 2002) and the total
perceived learning scores as measured by the Perceived CAP Learning Scale (Rovai et al., 2009)
There should be no significant outliers. Outliers are data points within your sample that do not
follow a similar pattern to the other data points. Pearson's correlation coefficient, r, is sensitive to
outliers, meaning that outliers can have an exaggerated influence on the value of r. This can lead
to Pearson's correlation efficient not having a value that best represents the data as a whole.
Therefore, it is best if there are no outliers or that they are kept to a minimum.
2) Linearity: This assumption assumes the relationship between the two variables is linear.
Check for linearity using a scatterplot; a roughly straight line (no curve) indicates that the
assumption is tenable.
3) Homoscedasticity: This assumption assumes the variability in scores in both variables should
be similar. Check for homoscedasticity using a scatterplot; a cigar shape indicates that the
assumption is tenable.
See Figure 1.
Figure 1.
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Descriptive Statistics
This assignment required elements to be presented from the data set provided. An SPSS
analysis of the mean, median, standard deviation, variance, and range for community
connectedness and perceived learning were performed. See Table 1.
Table 1.
Descriptive Statistics for Community Connectedness and Perceived Learning Variable (N = 40)
M
Mdn
SD
V
Range
Community Connectedness
54.65
27.00
19.66
96.38
29
Perceived Learning
37.43
42.50
13.86
192.20
42
Results
Partial correlation was used to evaluate the null hypothesis that there is no significant
relationship between online university’s students’ sense of community and perceived learning,
after controlling for gender (N = 40). Preliminary analyses using a scatter plot were performed to
ensure no violations of the assumptions of linearity, bivariate normality, and homoscedasticity;
assumptions were found tenable. There was significant evidence to reject the null hypothesis
and conclude that there was a strong positive partial correlation between sense of community (M
= 54.65, SD = 19.66) and perceived learning (M = 37.43, SD = 13.86), while controlling for
gender (M = 1.50, SD = 0.51), r (39) = 0.91, p >.01. Higher levels of community are associated
with higher levels of perceived learning. Results of the zero order correlation yielded that there
was strong positive correlation between sense of community and perceived learning, r (38) = .89,
p<.0013, thus; indicating that controlling for gender had a minimal effect on the strength of the
relationship between the two variables.
SPSS CORRELATION & REGRESSION
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Research Question 2
Is there a statistically significant relationship between student’s sense of community and
their grade point average among students who are enrolled in the Introduction to Statistics
course?
Null Hypothesis 2
There is not a significant predictive relationship between student’s sense of community
and their grade point average (GPA) among students who are enrolled in the Introduction to
Statistics course.
Alternative Hypothesis 2
There is a significant predictive relationship between student’s sense of community and
their GPA among students who are enrolled in the Introduction to Statistics course.
Continuous Variables
Students’ total community score as measured by the Classroom Community Scale (Rovai,
2002)
Grade Point Average (GPA)
Test to be Used
Since we seek the relationship direction and strength of two variables, the Pearson’s
product coefficient is the appropriate tool for determining this second research question. A
linear regression analysis was conducted to evaluate the null hypothesis that university students’
sense of community cannot significantly predict their GPA. The objective of the research aligns
with the purpose of a bivariate linear regression. A simple linear regression: (1) determines the
proportion of the variation in the dependent variable explained by the independent variable; and
(2) predicts criterion variable values based on the predictor variable value (Warner, 2012).
SPSS CORRELATION & REGRESSION
Assumptions
Preliminary analyses using a scatter plot were performed to ensure no violations of the
assumptions of linearity, no significant outliers or influential points, independence of residuals,
and homoscedasticity; assumptions were found tenable. See Figure 2.
Figure 2.
Descriptive Statistics
This assignment required elements to be presented from the data set provided. An SPSS
analysis of the mean, median, standard deviation, variance, and range for community
connectedness and grade point average were performed. See Table 2.
Table 2.
Descriptive Statistics for Community Connectedness and Grade Point Average (N = 40)
M
Mdn
SD
V
Range
Community Connectedness
27.03
27.00
9.82
96.38
29.00
Grade Point Average
3.05
3.10
0.69
0.47
2.30
Results
7
SPSS CORRELATION & REGRESSION
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Pearson’s product coefficient was used to evaluate the null hypothesis that there is no
significant relationship between online university’s students’ sense of community and grade
point average (N = 40). Preliminary analyses using a scatter plot were performed to ensure no
violations of the assumptions of linearity, bivariate normality, and homoscedasticity;
assumptions were found tenable. There was significant evidence to reject the null hypothesis
and conclude that there was a moderately positive partial correlation between community
connectedness (M = 27.03, SD = 9.82) and grade point average (M = 3.05, SD = 0.69) r = 0.91, p
>.01. Higher levels of community are associated with higher levels of grade point average.
Effect Size
The effect size was determined using the formula for eta squared (t squared/t squared +
(N1+N2-2). In this case that means 16.482/16.482 + (40+40-2) = 271.59/271.59+78 =
271.59/341.59 = 0.80. Therefore, the Pearson correlation coefficient in this example, (r = .894)
suggests a strong correlation per the guidelines suggested by Cohen (1988).
SPSS CORRELATION & REGRESSION
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References
Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ:
Lawrence Earlbaum Associates.
Rovai, A.P., Wighting M.J.. Baker, J.D., & Grooms, L.D. (2009). Development of an instrument
to measure perceived cognitive, affective, and psychomotor (CAP) learning in traditional
and virtual classroom higher education settings. Internet and Higher Education, 12(1), 713.
Szapkiw, A. (2014). Spss assignment instructions. In Lynchburg, VA: Liberty University.
Retrieved from http://amandaszapkiw.com/elearning/writing/downloads/ReportingStatisical-Results-in-APA-Format.pdf
SPSS CORRELATION & REGRESSION
Appendix
GET
FILE='C:\Users\Deb\Documents\liberty\educ812\SPSS_Assignment_Data_Set.sav'.
DATASET NAME DataSet1 WINDOW=FRONT.
DESCRIPTIVES VARIABLES=Community_Connectedness_Scale
Perceived_CAP_Learning_Scale
/STATISTICS=MEAN STDDEV VARIANCE RANGE MIN MAX.
Descriptives
Notes
Output Created
17-SEP-2014 12:52:34
Comments
Data
C:\Users\Deb\Documents\liberty\educ81
2\SPSS_Assignment_Data_Set.sav
Active Dataset
DataSet1
Filter
<none>
Weight
<none>
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<none>
Input
N of Rows in Working
Data File
40
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Missing Value
Handling
Definition of Missing
User defined missing values are treated
as missing.
Cases Used
All non-missing data are used.
DESCRIPTIVES
VARIABLES=Community_Connectedne
ss_Scale
Perceived_CAP_Learning_Scale
Syntax
/STATISTICS=MEAN STDDEV
VARIANCE RANGE MIN MAX.
Processor Time
00:00:00.00
Elapsed Time
00:00:00.04
Resources
[DataSet1] C:\Users\Deb\Documents\liberty\educ812\SPSS_Assignment_Data_Set.sav
Descriptive Statistics
N
Range
Minimu
m
Maximu
m
Mean
Std.
Deviation
Community_Connected
ness_Scale
40
29
11
40
27.03
9.818
Perceived_CAP_Learni
ng_Scale
40
42
12
54
37.43
13.864
Valid N (listwise)
40
Descriptive Statistics
Variance
11
SPSS CORRELATION & REGRESSION
Community_Connectedness_Scale
96.384
Perceived_CAP_Learning_Scale
192.199
Valid N (listwise)
FREQUENCIES VARIABLES=Community_Connectedness_Scale
Perceived_CAP_Learning_Scale
/STATISTICS=MEAN MEDIAN
/ORDER=ANALYSIS.
Frequencies
Notes
Output Created
17-SEP-2014 12:57:53
Comments
Input
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Data
C:\Users\Deb\Documents\liberty\
educ812\SPSS_Assignment_Data_Set.sa
v
Active Dataset
DataSet1
Filter
<none>
Weight
<none>
Split File
<none>
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N of Rows in Working
Data File
40
Definition of Missing
User-defined missing values are treated
as missing.
Cases Used
Statistics are based on all cases with
valid data.
Missing Value
Handling
FREQUENCIES
VARIABLES=Community_Connectedne
ss_Scale
Perceived_CAP_Learning_Scale
Syntax
/STATISTICS=MEAN MEDIAN
/ORDER=ANALYSIS.
Processor Time
00:00:00.02
Elapsed Time
00:00:00.03
Resources
[DataSet1] C:\Users\Deb\Documents\liberty\educ812\SPSS_Assignment_Data_Set.sav
Statistics
Community_ Perceived_C
Connectednes AP_Learning
s_Scale
_Scale
Valid
40
40
0
0
Mean
27.03
37.43
Median
27.00
42.50
N
Missing
13
SPSS CORRELATION & REGRESSION
Frequency Table
Community_Connectedness_Scale
Frequency Percent
Valid
Percent
Cumulative
Percent
11
3
7.5
7.5
7.5
12
3
7.5
7.5
15.0
14
1
2.5
2.5
17.5
15
1
2.5
2.5
20.0
20
3
7.5
7.5
27.5
22
2
5.0
5.0
32.5
23
6
15.0
15.0
47.5
27
2
5.0
5.0
52.5
30
1
2.5
2.5
55.0
32
1
2.5
2.5
57.5
34
1
2.5
2.5
60.0
35
4
10.0
10.0
70.0
36
3
7.5
7.5
77.5
37
5
12.5
12.5
90.0
Valid
14
SPSS CORRELATION & REGRESSION
38
1
2.5
2.5
92.5
40
3
7.5
7.5
100.0
40
100.0
100.0
Total
Perceived_CAP_Learning_Scale
Frequency Percent
Valid
Percent
Cumulative
Percent
12
1
2.5
2.5
2.5
14
1
2.5
2.5
5.0
15
1
2.5
2.5
7.5
16
2
5.0
5.0
12.5
18
1
2.5
2.5
15.0
19
1
2.5
2.5
17.5
22
1
2.5
2.5
20.0
Valid 25
2
5.0
5.0
25.0
27
3
7.5
7.5
32.5
29
2
5.0
5.0
37.5
32
1
2.5
2.5
40.0
35
1
2.5
2.5
42.5
40
3
7.5
7.5
50.0
45
4
10.0
10.0
60.0
47
3
7.5
7.5
67.5
15
SPSS CORRELATION & REGRESSION
48
2
5.0
5.0
72.5
50
3
7.5
7.5
80.0
51
2
5.0
5.0
85.0
52
1
2.5
2.5
87.5
53
2
5.0
5.0
92.5
54
3
7.5
7.5
100.0
40
100.0
100.0
Total
FREQUENCIES VARIABLES=Community_Connectedness_Scale GPA
/STATISTICS=STDDEV VARIANCE RANGE MINIMUM MAXIMUM MEAN MEDIAN
MODE
/ORDER=ANALYSIS.
Frequencies
Notes
Output Created
17-SEP-2014 13:01:48
Comments
Input
Data
C:\Users\Deb\Documents\liberty\
educ812\SPSS_Assignment_Data_Set.sa
v
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Active Dataset
DataSet1
Filter
<none>
Weight
<none>
Split File
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N of Rows in Working
Data File
40
Definition of Missing
User-defined missing values are treated
as missing.
Cases Used
Statistics are based on all cases with
valid data.
Missing Value
Handling
FREQUENCIES
VARIABLES=Community_Connectedne
ss_Scale GPA
Syntax
/STATISTICS=STDDEV VARIANCE
RANGE MINIMUM MAXIMUM
MEAN MEDIAN MODE
/ORDER=ANALYSIS.
Processor Time
00:00:00.00
Elapsed Time
00:00:00.00
Resources
[DataSet1] C:\Users\Deb\Documents\liberty\educ812\SPSS_Assignment_Data_Set.sav
Statistics
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SPSS CORRELATION & REGRESSION
Community_
Connectednes
s_Scale
Valid
GPA
40
40
0
0
Mean
27.03
3.0500
Median
27.00
3.1000
23
4.00
9.818
.68687
96.384
.472
Range
29
2.30
Minimum
11
1.70
Maximum
40
4.00
N
Missing
Mode
Std. Deviation
Variance
Frequency Table
Community_Connectedness_Scale
Frequency Percent
Valid
Percent
Cumulative
Percent
11
3
7.5
7.5
7.5
12
3
7.5
7.5
15.0
Valid
18
SPSS CORRELATION & REGRESSION
14
1
2.5
2.5
17.5
15
1
2.5
2.5
20.0
20
3
7.5
7.5
27.5
22
2
5.0
5.0
32.5
23
6
15.0
15.0
47.5
27
2
5.0
5.0
52.5
30
1
2.5
2.5
55.0
32
1
2.5
2.5
57.5
34
1
2.5
2.5
60.0
35
4
10.0
10.0
70.0
36
3
7.5
7.5
77.5
37
5
12.5
12.5
90.0
38
1
2.5
2.5
92.5
40
3
7.5
7.5
100.0
40
100.0
100.0
Total
GPA
Frequency Percent
Valid
Percent
Cumulative
Percent
1.70
2
5.0
5.0
5.0
Valid 1.90
2
5.0
5.0
10.0
2.10
1
2.5
2.5
12.5
19
SPSS CORRELATION & REGRESSION
2.30
2
5.0
5.0
17.5
2.40
2
5.0
5.0
22.5
2.50
1
2.5
2.5
25.0
2.60
2
5.0
5.0
30.0
2.70
2
5.0
5.0
35.0
2.80
1
2.5
2.5
37.5
2.90
1
2.5
2.5
40.0
3.00
4
10.0
10.0
50.0
3.20
3
7.5
7.5
57.5
3.30
1
2.5
2.5
60.0
3.40
2
5.0
5.0
65.0
3.50
3
7.5
7.5
72.5
3.60
1
2.5
2.5
75.0
3.70
3
7.5
7.5
82.5
3.80
2
5.0
5.0
87.5
4.00
5
12.5
12.5
100.0
Total
40
100.0
100.0
T-TEST PAIRS=Community_Connectedness_Scale WITH GPA (PAIRED)
/CRITERIA=CI(.9500)
/MISSING=ANALYSIS.
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SPSS CORRELATION & REGRESSION
T-Test
Notes
Output Created
17-SEP-2014 13:10:56
Comments
Input
Data
C:\Users\Deb\Documents\liberty\
educ812\SPSS_Assignment_Data_Set.sa
v
Active Dataset
DataSet1
Filter
<none>
Weight
<none>
Split File
<none>
N of Rows in Working
Data File
40
Definition of Missing
User defined missing values are treated
as missing.
Cases Used
Statistics for each analysis are based on
the cases with no missing or out-of-range
data for any variable in the analysis.
Missing Value
Handling
T-TEST
PAIRS=Community_Connectedness_Sca
le WITH GPA (PAIRED)
Syntax
/CRITERIA=CI(.9500)
/MISSING=ANALYSIS.
Resources
Processor Time
00:00:00.02
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SPSS CORRELATION & REGRESSION
Elapsed Time
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[DataSet1] C:\Users\Deb\Documents\liberty\educ812\SPSS_Assignment_Data_Set.sav
Paired Samples Statistics
Mean
Community_Connected
Pair 1 ness_Scale
GPA
N
Std.
Deviation
27.03
40
9.818
1.552
3.0500
40
.68687
.10860
Paired Samples Correlations
N
Pair 1
Community_Connected
ness_Scale & GPA
Std. Error
Mean
Correlatio
n
40
.908
Sig.
.000
Paired Samples Test
Paired Differences
22
SPSS CORRELATION & REGRESSION
Mean
Std.
Deviation
Std. Error
Mean
23
95%
Confidence
Interval of
the
Difference
Lower
Pair 1
Community_Connected 23.97500
ness_Scale - GPA
9.19849
1.45441
21.03318
Paired Samples Test
Paired
Differences
t
df
Sig. (2-tailed)
95%
Confidence
Interval of the
Difference
Upper
Pair 1
Community_Connectednes
s_Scale - GPA
26.91682
16.484
39
PARTIAL CORR
/VARIABLES=Perceived_CAP_Learning_Scale Community_Scale_Total BY Sex
/SIGNIFICANCE=TWOTAIL
/STATISTICS=DESCRIPTIVES
/MISSING=LISTWISE.
.000
SPSS CORRELATION & REGRESSION
Partial Corr
Notes
Output Created
17-SEP-2014 12:07:20
Comments
Input
Data
C:\Users\Deb\Documents\liberty\
educ812\SPSS_Assignment_Data_Set.sa
v
Active Dataset
DataSet1
Filter
<none>
Weight
<none>
Split File
<none>
N of Rows in Working
Data File
40
Definition of Missing
User defined missing values are treated
as missing.
Cases Used
Statistics are based on cases with no
missing data for any variable listed.
Missing Value
Handling
PARTIAL CORR
/VARIABLES=Perceived_CAP_Learnin
g_Scale Community_Scale_Total BY
Sex
Syntax
/SIGNIFICANCE=TWOTAIL
/STATISTICS=DESCRIPTIVES
/MISSING=LISTWISE.
Resources
Processor Time
00:00:00.00
24
SPSS CORRELATION & REGRESSION
Elapsed Time
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[DataSet1] C:\Users\Deb\Documents\liberty\educ812\SPSS_Assignment_Data_Set.sav
Descriptive Statistics
Mean
Std.
Deviation
N
Perceived_CAP_Learni
ng_Scale
37.43
13.864
40
Community_Scale_Tot
al
54.65
19.657
40
1.50
.506
40
Sex
Correlations
Control Variables
Perceived_C Community_
AP_Learning Scale_Total
_Scale
Correlation
Sex
Perceived_CAP_Learni Significance (2ng_Scale
tailed)
df
Community_Scale_Tota Correlation
1.000
.910
.
.000
0
37
.910
1.000
25
SPSS CORRELATION & REGRESSION
l
Significance (2tailed)
df
.000
.
37
0
GRAPH
/SCATTERPLOT(BIVAR)=Perceived_CAP_Learning_Scale WITH
Community_Connectedness_Scale
/MISSING=LISTWISE.
Graph
Notes
Output Created
17-SEP-2014 12:07:42
Comments
Input
Data
C:\Users\Deb\Documents\liberty\
educ812\SPSS_Assignment_Data_Set.sa
v
Active Dataset
DataSet1
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N of Rows in Working
Data File
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GRAPH
/SCATTERPLOT(BIVAR)=Perceived_C
AP_Learning_Scale WITH
Community_Connectedness_Scale
Syntax
/MISSING=LISTWISE.
Processor Time
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Elapsed Time
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Resources
[DataSet1] C:\Users\Deb\Documents\liberty\educ812\SPSS_Assignment_Data_Set.sav
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SPSS CORRELATION & REGRESSION
CORRELATIONS
/VARIABLES=Community_Connectedness_Scale GPA
/PRINT=TWOTAIL NOSIG
/STATISTICS DESCRIPTIVES
/MISSING=PAIRWISE.
28
SPSS CORRELATION & REGRESSION
Correlations
Notes
Output Created
17-SEP-2014 12:21:31
Comments
Input
Data
C:\Users\Deb\Documents\liberty\
educ812\SPSS_Assignment_Data_Set.sa
v
Active Dataset
DataSet1
Filter
<none>
Weight
<none>
Split File
<none>
N of Rows in Working
Data File
40
Definition of Missing
User-defined missing values are treated
as missing.
Cases Used
Statistics for each pair of variables are
based on all the cases with valid data for
that pair.
Missing Value
Handling
CORRELATIONS
Syntax
/VARIABLES=Community_Connectedn
ess_Scale GPA
/PRINT=TWOTAIL NOSIG
/STATISTICS DESCRIPTIVES
/MISSING=PAIRWISE.
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SPSS CORRELATION & REGRESSION
Processor Time
00:00:00.03
Elapsed Time
00:00:00.06
Resources
[DataSet1] C:\Users\Deb\Documents\liberty\educ812\SPSS_Assignment_Data_Set.sav
Descriptive Statistics
Mean
Community_Connected
ness_Scale
GPA
Std.
Deviation
N
27.03
9.818
40
3.0500
.68687
40
Correlations
Community_
Connectedne
ss_Scale
Pearson
Correlation
1
Community_Connected
ness_Scale
Sig. (2-tailed)
N
GPA
Pearson
Correlation
GPA
.908**
.000
40
40
.908**
1
30
SPSS CORRELATION & REGRESSION
Sig. (2-tailed)
N
.000
40
40
**. Correlation is significant at the 0.01 level (2-tailed).
GRAPH
/SCATTERPLOT(BIVAR)=GPA WITH Community_Connectedness_Scale
/MISSING=LISTWISE.
Graph
Notes
Output Created
17-SEP-2014 12:22:21
Comments
Input
Data
C:\Users\Deb\Documents\liberty\
educ812\SPSS_Assignment_Data_Set.sa
v
Active Dataset
DataSet1
Filter
<none>
Weight
<none>
Split File
<none>
31
SPSS CORRELATION & REGRESSION
N of Rows in Working
Data File
40
GRAPH
/SCATTERPLOT(BIVAR)=GPA
WITH
Community_Connectedness_Scale
Syntax
/MISSING=LISTWISE.
Processor Time
00:00:00.31
Elapsed Time
00:00:00.39
Resources
[DataSet1] C:\Users\Deb\Documents\liberty\educ812\SPSS_Assignment_Data_Set.sav
32
SPSS CORRELATION & REGRESSION
33