SPSS Correlation & Regression Assignment

SPSS CORRELATIONREGRESSION 1

Deborah Davis

Liberty University

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 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)

Continuous Covariate

Gender

Test to be Used

Since we have two continuous variables, and want to statistically control another variable, the PAIRED SAMPLE T-TEST is the appropriate tool for conducting a partial correlation for this research question.

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. See Figure 1.

Figure 1.

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 / 27.03 / 27.00 / 9.82 / 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 = 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 perfect positive correlation between sense of community and perceived learning, r = 1.00, thus; indicating that controlling for gender had a minimal effect on the strength of the relationship between the two variables.

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 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 relationship between student’s sense of community and their GPAamong 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.

Assumptions

Figure 2.

Descriptive Statistics

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

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.

References

Rovai, A.P., WightingM.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), 7-13.

Szapkiw, A. (2014). Spss assignment instructions. In Lynchburg, VA: Liberty University. Retrieved from

Appendix

GET

FILE='C:\Users\Ken\Documents\liberty\educ712\SPSS_Assignment_Data_Set.sav'.

DATASET NAME DataSet1 WINDOW=FRONT.

DESCRIPTIVES VARIABLES=Community_Connectedness_ScalePerceived_CAP_Learning_Scale

/STATISTICS=MEAN STDDEV VARIANCE RANGE MIN MAX.

Descriptives

Notes
Output Created / 11-FEB-2014 12:52:34
Comments
Input / Data / C:\Users\Ken\Documents\liberty\educ712\SPSS_Assignment_Data_Set.sav
Active Dataset / DataSet1
Filter / <none>
Weight / <none>
Split File / <none>
N of Rows in Working Data File / 40
Missing Value Handling / Definition of Missing / User defined missing values are treated as missing.
Cases Used / All non-missing data are used.
Syntax / DESCRIPTIVES VARIABLES=Community_Connectedness_ScalePerceived_CAP_Learning_Scale
/STATISTICS=MEAN STDDEV VARIANCE RANGE MIN MAX.
Resources / Processor Time / 00:00:00.00
Elapsed Time / 00:00:00.04

[DataSet1] C:\Users\Ken\Documents\liberty\educ712\SPSS_Assignment_Data_Set.sav

Descriptive Statistics
N / Range / Minimum / Maximum / Mean / Std. Deviation
Community_Connectedness_Scale / 40 / 29 / 11 / 40 / 27.03 / 9.818
Perceived_CAP_Learning_Scale / 40 / 42 / 12 / 54 / 37.43 / 13.864
Valid N (listwise) / 40
Descriptive Statistics
Variance
Community_Connectedness_Scale / 96.384
Perceived_CAP_Learning_Scale / 192.199
Valid N (listwise)

FREQUENCIES VARIABLES=Community_Connectedness_ScalePerceived_CAP_Learning_Scale

/STATISTICS=MEAN MEDIAN

/ORDER=ANALYSIS.

Frequencies

Notes
Output Created / 11-FEB-2014 12:57:53
Comments
Input / Data / C:\Users\Ken\Documents\liberty\educ712\SPSS_Assignment_Data_Set.sav
Active Dataset / DataSet1
Filter / <none>
Weight / <none>
Split File / <none>
N of Rows in Working Data File / 40
Missing Value Handling / Definition of Missing / User-defined missing values are treated as missing.
Cases Used / Statistics are based on all cases with valid data.
Syntax / FREQUENCIES VARIABLES=Community_Connectedness_ScalePerceived_CAP_Learning_Scale
/STATISTICS=MEAN MEDIAN
/ORDER=ANALYSIS.
Resources / Processor Time / 00:00:00.02
Elapsed Time / 00:00:00.03

[DataSet1] C:\Users\Ken\Documents\liberty\educ712\SPSS_Assignment_Data_Set.sav

Statistics
Community_Connectedness_Scale / Perceived_CAP_Learning_Scale
N / Valid / 40 / 40
Missing / 0 / 0
Mean / 27.03 / 37.43
Median / 27.00 / 42.50

Frequency Table

Community_Connectedness_Scale
Frequency / Percent / Valid Percent / Cumulative Percent
Valid / 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
38 / 1 / 2.5 / 2.5 / 92.5
40 / 3 / 7.5 / 7.5 / 100.0
Total / 40 / 100.0 / 100.0
Perceived_CAP_Learning_Scale
Frequency / Percent / Valid Percent / Cumulative Percent
Valid / 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
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
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
Total / 40 / 100.0 / 100.0

FREQUENCIES VARIABLES=Community_Connectedness_Scale GPA

/STATISTICS=STDDEV VARIANCE RANGE MINIMUM MAXIMUM MEAN MEDIAN MODE

/ORDER=ANALYSIS.

Frequencies

Notes
Output Created / 11-FEB-2014 13:01:48
Comments
Input / Data / C:\Users\Ken\Documents\liberty\educ712\SPSS_Assignment_Data_Set.sav
Active Dataset / DataSet1
Filter / <none>
Weight / <none>
Split File / <none>
N of Rows in Working Data File / 40
Missing Value Handling / Definition of Missing / User-defined missing values are treated as missing.
Cases Used / Statistics are based on all cases with valid data.
Syntax / FREQUENCIES VARIABLES=Community_Connectedness_Scale GPA
/STATISTICS=STDDEV VARIANCE RANGE MINIMUM MAXIMUM MEAN MEDIAN MODE
/ORDER=ANALYSIS.
Resources / Processor Time / 00:00:00.00
Elapsed Time / 00:00:00.00

[DataSet1] C:\Users\Ken\Documents\liberty\educ712\SPSS_Assignment_Data_Set.sav

Statistics
Community_Connectedness_Scale / GPA
N / Valid / 40 / 40
Missing / 0 / 0
Mean / 27.03 / 3.0500
Median / 27.00 / 3.1000
Mode / 23 / 4.00
Std. Deviation / 9.818 / .68687
Variance / 96.384 / .472
Range / 29 / 2.30
Minimum / 11 / 1.70
Maximum / 40 / 4.00

Frequency Table

Community_Connectedness_Scale
Frequency / Percent / Valid Percent / Cumulative Percent
Valid / 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
38 / 1 / 2.5 / 2.5 / 92.5
40 / 3 / 7.5 / 7.5 / 100.0
Total / 40 / 100.0 / 100.0
GPA
Frequency / Percent / Valid Percent / Cumulative Percent
Valid / 1.70 / 2 / 5.0 / 5.0 / 5.0
1.90 / 2 / 5.0 / 5.0 / 10.0
2.10 / 1 / 2.5 / 2.5 / 12.5
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.

T-Test

Notes
Output Created / 11-FEB-2014 13:10:56
Comments
Input / Data / C:\Users\Ken\Documents\liberty\educ712\SPSS_Assignment_Data_Set.sav
Active Dataset / DataSet1
Filter / <none>
Weight / <none>
Split File / <none>
N of Rows in Working Data File / 40
Missing Value Handling / 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.
Syntax / T-TEST PAIRS=Community_Connectedness_Scale WITH GPA (PAIRED)
/CRITERIA=CI(.9500)
/MISSING=ANALYSIS.
Resources / Processor Time / 00:00:00.02
Elapsed Time / 00:00:00.06

[DataSet1] C:\Users\Ken\Documents\liberty\educ712\SPSS_Assignment_Data_Set.sav

Paired Samples Statistics
Mean / N / Std. Deviation / Std. Error Mean
Pair 1 / Community_Connectedness_Scale / 27.03 / 40 / 9.818 / 1.552
GPA / 3.0500 / 40 / .68687 / .10860
Paired Samples Correlations
N / Correlation / Sig.
Pair 1 / Community_Connectedness_Scale & GPA / 40 / .908 / .000
Paired Samples Test
Paired Differences
Mean / Std. Deviation / Std. Error Mean / 95% Confidence Interval of the Difference
Lower
Pair 1 / Community_Connectedness_Scale - GPA / 23.97500 / 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_Connectedness_Scale - GPA / 26.91682 / 16.484 / 39 / .000

PARTIAL CORR

/VARIABLES=Perceived_CAP_Learning_ScaleCommunity_Scale_Total BY Sex

/SIGNIFICANCE=TWOTAIL

/STATISTICS=DESCRIPTIVES

/MISSING=LISTWISE.

Partial Corr

Notes
Output Created / 11-FEB-2014 12:07:20
Comments
Input / Data / C:\Users\Ken\Documents\liberty\educ712\SPSS_Assignment_Data_Set.sav
Active Dataset / DataSet1
Filter / <none>
Weight / <none>
Split File / <none>
N of Rows in Working Data File / 40
Missing Value Handling / 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.
Syntax / PARTIAL CORR
/VARIABLES=Perceived_CAP_Learning_ScaleCommunity_Scale_Total BY Sex
/SIGNIFICANCE=TWOTAIL
/STATISTICS=DESCRIPTIVES
/MISSING=LISTWISE.
Resources / Processor Time / 00:00:00.00
Elapsed Time / 00:00:00.01

[DataSet1] C:\Users\Ken\Documents\liberty\educ712\SPSS_Assignment_Data_Set.sav

Descriptive Statistics
Mean / Std. Deviation / N
Perceived_CAP_Learning_Scale / 37.43 / 13.864 / 40
Community_Scale_Total / 54.65 / 19.657 / 40
Sex / 1.50 / .506 / 40
Correlations
Control Variables / Perceived_CAP_Learning_Scale / Community_Scale_Total
Sex / Perceived_CAP_Learning_Scale / Correlation / 1.000 / .910
Significance (2-tailed) / . / .000
df / 0 / 37
Community_Scale_Total / Correlation / .910 / 1.000
Significance (2-tailed) / .000 / .
df / 37 / 0

GRAPH

/SCATTERPLOT(BIVAR)=Perceived_CAP_Learning_Scale WITH Community_Connectedness_Scale

/MISSING=LISTWISE.

Graph

Notes
Output Created / 11-FEB-2014 12:07:42
Comments
Input / Data / C:\Users\Ken\Documents\liberty\educ712\SPSS_Assignment_Data_Set.sav
Active Dataset / DataSet1
Filter / <none>
Weight / <none>
Split File / <none>
N of Rows in Working Data File / 40
Syntax / GRAPH
/SCATTERPLOT(BIVAR)=Perceived_CAP_Learning_Scale WITH Community_Connectedness_Scale
/MISSING=LISTWISE.
Resources / Processor Time / 00:00:00.31
Elapsed Time / 00:00:00.58

[DataSet1] C:\Users\Ken\Documents\liberty\educ712\SPSS_Assignment_Data_Set.sav

CORRELATIONS

/VARIABLES=Community_Connectedness_Scale GPA

/PRINT=TWOTAIL NOSIG

/STATISTICS DESCRIPTIVES

/MISSING=PAIRWISE.

Correlations

Notes
Output Created / 11-FEB-2014 12:21:31
Comments
Input / Data / C:\Users\Ken\Documents\liberty\educ712\SPSS_Assignment_Data_Set.sav
Active Dataset / DataSet1
Filter / <none>
Weight / <none>
Split File / <none>
N of Rows in Working Data File / 40
Missing Value Handling / 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.
Syntax / CORRELATIONS
/VARIABLES=Community_Connectedness_Scale GPA
/PRINT=TWOTAIL NOSIG
/STATISTICS DESCRIPTIVES
/MISSING=PAIRWISE.
Resources / Processor Time / 00:00:00.03
Elapsed Time / 00:00:00.06

[DataSet1] C:\Users\Ken\Documents\liberty\educ712\SPSS_Assignment_Data_Set.sav

Descriptive Statistics
Mean / Std. Deviation / N
Community_Connectedness_Scale / 27.03 / 9.818 / 40
GPA / 3.0500 / .68687 / 40
Correlations
Community_Connectedness_Scale / GPA
Community_Connectedness_Scale / Pearson Correlation / 1 / .908**
Sig. (2-tailed) / .000
N / 40 / 40
GPA / Pearson Correlation / .908** / 1
Sig. (2-tailed) / .000
N / 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 / 11-FEB-2014 12:22:21
Comments
Input / Data / C:\Users\Ken\Documents\liberty\educ712\SPSS_Assignment_Data_Set.sav
Active Dataset / DataSet1
Filter / <none>
Weight / <none>
Split File / <none>
N of Rows in Working Data File / 40
Syntax / GRAPH
/SCATTERPLOT(BIVAR)=GPA WITH Community_Connectedness_Scale
/MISSING=LISTWISE.
Resources / Processor Time / 00:00:00.31
Elapsed Time / 00:00:00.39

[DataSet1] C:\Users\Ken\Documents\liberty\educ712\SPSS_Assignment_Data_Set.sav