SPSS Final Exam Assignment

SPSS FINAL EXAM1

SPSS Final Exam Assignment

Deborah Davis

Liberty University

Purpose

The purpose of this document is to provide a response to the requirements of the Final Exam in SPSS that covers all elements of the Advanced Educational Statistics course with Dr. Amanda Rockinson-Szapkiw at Liberty University Online during Fall of 2014. The research scenario was given as part of the assignment, and generally depicts university students’ intrinsic religious commitment as measured by the Religious Orientation Scale–Revised (Gorsuch & McPherson, 1989) subscale and faith development as measured by the Faith Development Scale (FDS; Leak, Loucks, & Bowlin, 1999).

Structure

In that there are three research questions to this assignment and multiple sections to each of them, and will only use the first three levels of headings, and they will be separated by the requirements within each aspect.

Research Question Case 1

What is the relationship between university students’ intrinsic religious commitment as measured by the Religious Orientation Scale–Revised (Gorsuch & McPherson, 1989) subscale and faith development as measured by the Faith Development Scale (FDS; Leak, Loucks, & Bowlin,1999)?

Null hypothesis H00.

There is no statistically significant relationship between university students’ intrinsic religious commitment as measured by the Religious Orientation Scale–Revised (Gorsuch & McPherson, 1989) subscale and faith development as measured by the Faith Development Scale (FDS; Leak, Loucks, & Bowlin, 999).

Alternative hypothesis H01.

There is a statistically significant relationship between university students’ intrinsic religious commitment as measured by the Religious Orientation Scale–Revised (Gorsuch & McPherson, 1989) subscale and faith development as measured by the Faith Development Scale (FDS; Leak, Loucks, & Bowlin, 999).

Variables.

In a correlation study, “there is no clear justification for designating one of these variables as a predictor; the choice . . . is arbitrary” (Warner, 2008, p. 260)

Variable of interest – interval/ratio - religious commitment

Variable of interest – interval/ratio - faith development

Test to be used.

“Pearson r is typically used to describe the strength of the linear relationship between two quantitative variables” (Warner, 2008, p. 255). In that this case desires to determine the degree of relationship between the two variables, Pearson r would be the appropriate test.

Assumptions.

For the Pearson r test, an assumption of independence is required. Further, an assumption of distribution that scores are quantitative and normally distributed is also required. An assumption of relationship provides that that is a linear relationship between the variables. Also, the scores require a bivariate normal distribution. There is also an assumption of homogeneity between the variables. Preliminary analysis using a histogram was performed to ensure no violations of the assumptions of linearity, and bivariate normality; assumptions of normality were found not tenable in the variable of intrinsic religious commitment. See Figures 1 and 2.

Figure 1

Figure 2

A scatterplot was performed to determine linearity and homoscedasticity. The cigar shape was extremely broad and the line was generally straight indicating the assumptions of linearity and homoscedasticity are met. The scatterplot in Figure 3 also indicates and absence of significant outliers. See Figure 3.

Figure 3.

Results.

A Pearson’s r correlation was used to evaluate the null hypothesis that there is no statistically significant relationship between university students’ intrinsic religious commitment as measured by the Religious Orientation Scale–Revised (Gorsuch & McPherson, 1989) subscale and faith development as measured by the Faith Development Scale (FDS; Leak, Loucks, & Bowlin, 999)(N =40).With the Pearson r there is no control variable, and because this test was between two variables, a two-tailed correlation was used to evaluate the relationship. The results of the Pearon r test(r (39) = 0.86, p < .01)showed significant evidence to reject the null hypothesis. There was a strong positive relationship between intrinsic religious commitment as measured by the Religious Orientation Scale–Revised (Gorsuch & McPherson, 1989) (M=29.95, SD=6.74) and faith development as measured by the Faith Development Scale (FDS; Leak, Loucks, & Bowlin, 999) (M=2.40, SD=1.06), r (39) = 0.86, p < .01.

An SPSS analysis of the mean, standard deviation, and group number for religious orientation (M = 29.95, SD = 6.74, n = 40), was performed against faith development (M = 2.40, SD = 1.06, n =40) as a paired sample (M = -27.55, SD = 5.86, N = 40). See Table 1 for purposes of clarity. The observed power was 0.86. This showed a strong, positive correlation between the two.

Table 1.

Descriptive Statistics for Religious Orientation and Faith Development (N = 40)

n / M / SD
Religious Orientation / 40 / 29.95 / 6.74
Faith Development / 40 / 2.40 / 1.06
Total / -27.55 / 5.86

Research Question Case 2

Is there a statistically significant difference in students’ Faith Development Scale (FDS; Leak, Loucks, & Bowlin, 1999) from the time of entrance to now?

Null hypothesis H00.

There is no statistically significant difference in students’ Faith Development Scale (FDS; Leak, Loucks, & Bowlin, 1999) from the time of entrance to now.

Alternative hypothesis H01.

There is a statistically significant difference in students’ Faith Development Scale (FDS; Leak, Loucks, & Bowlin, 1999) from the time of entrance to now.

Test to be used.

When scores come from a repeated measures study, the paired samples t test is the appropriate tool to evaluate the statistically significant difference (Warner, 2008, p. 1029).

Assumptions

For the paired samples t test, a boxplot will test for extreme outliers, and the assumption normality is tested though “the t-test is robust over moderate violations of this assumption” (Szapkiw, 2012, p. 20). While parametric tests generally require an assumption of equal variances, “Equality of variance does not apply here as two populations are not being examined” (Szapkiw, 2012, p. 20).

Preliminary analyses using a histogram were performed to ensure no violations of the assumption of normality, and normality was found not tenable for either of the variables. However, when the distribution is not heavily skewed and the sample size is small, a relatively valid p value is still likely to be produced. See figures 4and 5.

Figure 4

Figure 5

Results

The paired samples t-test reflected a p value of less than .01 thus there is a significant difference between the scores of the entrance exam and current faith developmentscores t (39) = 0.63, p < .01 and reason to reject the null hypothesis. The descriptive results from an SPSS analysis of the mean, standard deviation, and group number for entrance exam faith score (M = 1.30, SD = 1.04, N = 40), was performed against faith development (M = 2.40, SD = 1.06, N =40) as a paired sample (M = 1.10, SD = 0.90, N = 40). See Table 2.

Table 2.

Descriptive Statistics for Religious Orientation and Faith Development (N = 40)

N / M / SD
Entrance Faith / 40 / 1.30 / 1.04
Faith Development / 40 / 2.40 / 1.06
Total / 1.10 / 0.90

Research Question Case 3

Do university students differ in terms of faith development as measured by the Faith Development Scale (Leak, Loucks, & Bowlin, 1999) and their sense of community score as measured by the Classroom Community Scale (Rovai, 2002) based their choice of delivery environment (online, blended)?

Null hypothesis H00.

There is no statistically significant difference in university students in terms of faith development as measured by the Faith Development Scale (Leak, Loucks, & Bowlin, 1999) and their sense of community score as measured by the Classroom Community Scale (Rovai, 2002) based their choice of delivery environment (online, blended).

Null hypothesis H01.

There is no statistically significant difference in university students in terms of faith development as measured by the Faith Development Scale (Leak, Loucks, & Bowlin, 1999) based on choice of delivery environment (online, blended).

Null hypothesis H02.

There is no statistically significant difference in university students in terms of sense of community as measured by the Classroom Community Scale (Rovai, 2002) based on choise of delivery environment (online, blended).

Alternative hypothesis H01.

Online and blended course students differ statistically in terms of faith development as measured by the Faith Development Scale (Leak, Loucks, & Bowlin, 1999) and their sense of community score as measured by the Classroom Community Scale (Rovai, 2002).

Alternative hypothesis H02.

Online and blended course students differ statistically in terms of faith development as measured by the Faith Development Scale (Leak, Loucks, & Bowlin, 1999).

Alternative hypothesis H03.

Online and blended course students differ statistically in their sense of community score as measured by the Classroom Community Scale (Rovai, 2002).

Dependent Variables.

Delivery environment (online, blended) -- nominal

Independent Variables.

Faith Development Scale – an interval/ratio scale

Community Connectedness Scale – an interval/ratio scale

Test to be used.

Considering there are two independent interval/ratio variables and two groups within one dependent nominal variable, the appropriate test to evaluation would be a one-way multivariate analysis of variance (MANOVA).

Assumptions.

Assumptions appropriate to the one-way MANOVA analysis include: extreme outliers, univariate normality, multivariate normality, multicolinearity and singularity, linearity, equal variances, and homogeneity of variance-covariance (Szapkiw, 2012, p. 31). Box-plots were used to test for extreme outliers. Histograms were used to test for normality, with a standard bell-curve indicating normality. Multivariate normality is tested with Mahalanobis distance. Correlation matrixes were checked for multicolinearity and singularity. Scatterplots were generated to test for linearity. Levene’s test is used to determine equal variances. Box’s M confirms the tenability of homogeneity of variance covariance (Szapkiw, 2012, p. 31). While assumptions of normality were found tenable as regards the faith development scale, assumptions of normality were found not tenable as regards the community connectedness scale. The general line affect and broad cigar shape of the scatterplot indicate that linearity and homoscedasticity are tenable. See Figures 7, 8, and 9. Therefore a requirement of more robust evaluation is required. The box plot shown in Figure 10 indicates extreme outliers in the community connectedness scale. Homogeneity of variance-covariance was evaluated using Box M’s as Box’s test M = 4.38, F (3, 115051.19) = 1.37, p = .025. A significance level of less than .05 indicates that this assumption is not tenable.

Figure 7

Figure 8

Figure 9

Figure 10

Results.

A one-way multivariate analysis of variance (MANOVA) was conducted to investigate the effect of course differences (i.e. online, blended) in the combination of community connectedness and the faith community scale. The pooled means and standard deviations for the community connectedness scale (M = 27.03, SD = 9.82, N = 40) against online (M = 29.65, SD = 9.19, n = 23) and blended (M = 23.47, SD = 9.77, n = 17) course choices and the faith community scale (M = 2.40, SD = 1.06, N = 40) against online (M = 2.61, SD = 1.08, n = 23) and blended (M = 2.12, SD = 0.99, n = 17) course choices. Disaggregated means and standard deviations for online (n = 23) and blended (n = 17) are shown in Table 3.

Table 3

Descriptive Statistics on Dependent Variable disaggregated by types of course (N = 40)
Variable / Online (n=23) / Blended (n=17) / Total (N=40)
M / SD / M / SD / M / SD
Community / 29.65 / 9.19 / 23.47 / 9.77 / 27.03 / 9.82
Faith / 2.61 / 1.08 / 2.12 / 0.99 / 2.40 / 1.06

Preliminary assumption testing was conducted. Independent sample Kolmogorov-Smimov test was conducted for normality with a Lilliefor’s correction, histograms and Shapiro-Wilk test for normality and a Mahalanobis distances. Normality for the both groups on both scales showed them found tenable at the .05 level. The results of the Levene’s test of equality of error provided evidence the assumption of homogeneity across groups wastenable for community connectedness F (1, 38) = 0.02, p = 0.90, and for faith community sense F (1, 38) = 0.73, p = 0.40. Consequently, Wilks’ Λ was used because these assumptions were found tenable. There was a statistically significance difference by type of program on the combined dependent variables, Wilks Λ = 0.90, F (2, 37) = 2.04, p = 0.40, partial ᾐ2 = 0.14, observed power = 0.39. The online students scored slightly higher on both the community connectedness scale and the faith connectedness than the blended students (see Table 3). Based on Cohen’s threshold of .01 for small, .06 for medium, and .14 for large, (Cohen, 1988) the effect sizes were large for the dependent variables. The effect size for learning was large.

References

Cohen, J., (1988).Statistical power analysis for the behavioral sciences, (2nd Ed.) Hillsdale, NJ: Lawrence Erlbaum.

Gorsuch, R. L., & McPherson, S. E. (1989). Intrinsic/extrinsic measurement: I/E-revised and single-item scales. Journal for the Scientific Study of Religion 28(348-354).

Leak, G.K., Loucks, A.A., & Bowlin, P. (1999). Development and initial validation of an objective measure of faith development. International Journal for the Psychology of Religion, 9(2), 105.

Rovai, A.P. (2001). Building classroom community at a distance: a case study. Educational Technology Research & Development, 49(4), 33-48. Doi: 10.1007/BF02504946

Warner, R. M. (2008). Applied statistics: From bivariate through multivariate techniques. Thousand Oaks, CA: Sage Publications

Appendix

FINAL – CASE 1 SPSS OUTPUT

GET

FILE='C:\Users\deb\Downloads\SPSS_Assignment_Data_Set(3) (1).sav'.

DATASET NAME DataSet1 WINDOW=FRONT.

CORRELATIONS

/VARIABLES=Intrinsic_Religious_Orientation_Scale Faith_Development_Scale

/PRINT=TWOTAIL NOSIG

/STATISTICS DESCRIPTIVES XPROD

/MISSING=PAIRWISE.

Correlations

Notes
Output Created / 09-OCT-2014 06:46:22
Comments
Input / Data / C:\Users\deb\Downloads\SPSS_Assignment_Data_Set(3) (1).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=Intrinsic_Religious_Orientation_Scale Faith_Development_Scale
/PRINT=TWOTAIL NOSIG
/STATISTICS DESCRIPTIVES XPROD
/MISSING=PAIRWISE.
Resources / Processor Time / 00:00:00.02
Elapsed Time / 00:00:00.05

[DataSet1] C:\Users\deb\Downloads\SPSS_Assignment_Data_Set(3) (1).sav

Descriptive Statistics
Mean / Std. Deviation / N
Intrinsic_Religious_Orientation_Scale / 29.95 / 6.737 / 40
Faith_Development_Scale / 2.40 / 1.057 / 40
Correlations
Intrinsic_Religious_Orientation_Scale / Faith_Development_Scale
Intrinsic_Religious_Orientation_Scale / Pearson Correlation / 1 / .856**
Sig. (2-tailed) / .000
Sum of Squares and Cross-products / 1769.900 / 237.800
Covariance / 45.382 / 6.097
N / 40 / 40
Faith_Development_Scale / Pearson Correlation / .856** / 1
Sig. (2-tailed) / .000
Sum of Squares and Cross-products / 237.800 / 43.600
Covariance / 6.097 / 1.118
N / 40 / 40
**. Correlation is significant at the 0.01 level (2-tailed).

* Chart Builder.

GGRAPH

/GRAPHDATASET NAME="graphdataset" VARIABLES=Faith_Development_Scale MISSING=LISTWISE REPORTMISSING=NO

/GRAPHSPEC SOURCE=INLINE.

BEGIN GPL

SOURCE: s=userSource(id("graphdataset"))

DATA: Faith_Development_Scale=col(source(s), name("Faith_Development_Scale"))

GUIDE: axis(dim(1), label("Faith_Development_Scale"))

GUIDE: axis(dim(2), label("Frequency"))

ELEMENT: interval(position(summary.count(bin.rect(Faith_Development_Scale))), shape.interior(shape.square))

ELEMENT: line(position(density.normal(Faith_Development_Scale)), color("Normal"))

END GPL.

GGraph

Notes
Output Created / 09-OCT-2014 06:51:01
Comments
Input / Data / C:\Users\deb\Downloads\SPSS_Assignment_Data_Set(3) (1).sav
Active Dataset / DataSet1
Filter / <none>
Weight / <none>
Split File / <none>
N of Rows in Working Data File / 40
Syntax / GGRAPH
/GRAPHDATASET NAME="graphdataset" VARIABLES=Faith_Development_Scale MISSING=LISTWISE REPORTMISSING=NO
/GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
SOURCE: s=userSource(id("graphdataset"))
DATA: Faith_Development_Scale=col(source(s), name("Faith_Development_Scale"))
GUIDE: axis(dim(1), label("Faith_Development_Scale"))
GUIDE: axis(dim(2), label("Frequency"))
ELEMENT: interval(position(summary.count(bin.rect(Faith_Development_Scale))), shape.interior(shape.square))
ELEMENT: line(position(density.normal(Faith_Development_Scale)), color("Normal"))
END GPL.
Resources / Processor Time / 00:00:02.17
Elapsed Time / 00:00:02.40

* Chart Builder.

GGRAPH

/GRAPHDATASET NAME="graphdataset" VARIABLES=Intrinsic_Religious_Orientation_Scale MISSING=LISTWISE REPORTMISSING=NO

/GRAPHSPEC SOURCE=INLINE.

BEGIN GPL

SOURCE: s=userSource(id("graphdataset"))

DATA: Intrinsic_Religious_Orientation_Scale=col(source(s), name("Intrinsic_Religious_Orientation_Scale"))

GUIDE: axis(dim(1), label("Intrinsic_Religious_Orientation_Scale"))

GUIDE: axis(dim(2), label("Frequency"))

ELEMENT: interval(position(summary.count(bin.rect(Intrinsic_Religious_Orientation_Scale))), shape.interior(shape.square))

ELEMENT: line(position(density.normal(Intrinsic_Religious_Orientation_Scale)), color("Normal"))

END GPL.

GGraph

Notes
Output Created / 09-OCT-2014 06:51:20
Comments
Input / Data / C:\Users\deb\Downloads\SPSS_Assignment_Data_Set(3) (1).sav
Active Dataset / DataSet1
Filter / <none>
Weight / <none>
Split File / <none>
N of Rows in Working Data File / 40
Syntax / GGRAPH
/GRAPHDATASET NAME="graphdataset" VARIABLES=Intrinsic_Religious_Orientation_Scale MISSING=LISTWISE REPORTMISSING=NO
/GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
SOURCE: s=userSource(id("graphdataset"))
DATA: Intrinsic_Religious_Orientation_Scale=col(source(s), name("Intrinsic_Religious_Orientation_Scale"))
GUIDE: axis(dim(1), label("Intrinsic_Religious_Orientation_Scale"))
GUIDE: axis(dim(2), label("Frequency"))
ELEMENT: interval(position(summary.count(bin.rect(Intrinsic_Religious_Orientation_Scale))), shape.interior(shape.square))
ELEMENT: line(position(density.normal(Intrinsic_Religious_Orientation_Scale)), color("Normal"))
END GPL.
Resources / Processor Time / 00:00:00.36
Elapsed Time / 00:00:00.49

* Chart Builder.

GGRAPH

/GRAPHDATASET NAME="graphdataset" VARIABLES=Intrinsic_Religious_Orientation_Scale Faith_Development_Scale MISSING=LISTWISE REPORTMISSING=NO

/GRAPHSPEC SOURCE=INLINE.

BEGIN GPL

SOURCE: s=userSource(id("graphdataset"))

DATA: Intrinsic_Religious_Orientation_Scale=col(source(s), name("Intrinsic_Religious_Orientation_Scale"))

DATA: Faith_Development_Scale=col(source(s), name("Faith_Development_Scale"))

GUIDE: axis(dim(1), label("Intrinsic_Religious_Orientation_Scale"))

GUIDE: axis(dim(2), label("Faith_Development_Scale"))

ELEMENT: point(position(Intrinsic_Religious_Orientation_Scale*Faith_Development_Scale))

END GPL.

GGraph

Notes
Output Created / 09-OCT-2014 06:51:44
Comments
Input / Data / C:\Users\deb\Downloads\SPSS_Assignment_Data_Set(3) (1).sav
Active Dataset / DataSet1
Filter / <none>
Weight / <none>
Split File / <none>
N of Rows in Working Data File / 40
Syntax / GGRAPH
/GRAPHDATASET NAME="graphdataset" VARIABLES=Intrinsic_Religious_Orientation_Scale Faith_Development_Scale MISSING=LISTWISE REPORTMISSING=NO
/GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
SOURCE: s=userSource(id("graphdataset"))
DATA: Intrinsic_Religious_Orientation_Scale=col(source(s), name("Intrinsic_Religious_Orientation_Scale"))
DATA: Faith_Development_Scale=col(source(s), name("Faith_Development_Scale"))
GUIDE: axis(dim(1), label("Intrinsic_Religious_Orientation_Scale"))
GUIDE: axis(dim(2), label("Faith_Development_Scale"))
ELEMENT: point(position(Intrinsic_Religious_Orientation_Scale*Faith_Development_Scale))
END GPL.
Resources / Processor Time / 00:00:00.36
Elapsed Time / 00:00:00.59

FINAL EXAM CASE 2

* Chart Builder.

GGRAPH

/GRAPHDATASET NAME="graphdataset" VARIABLES=Faith_Development_Scale MISSING=LISTWISE REPORTMISSING=NO

/GRAPHSPEC SOURCE=INLINE.

BEGIN GPL

SOURCE: s=userSource(id("graphdataset"))

DATA: Faith_Development_Scale=col(source(s), name("Faith_Development_Scale"))

DATA: id=col(source(s), name("$CASENUM"), unit.category())

COORD: rect(dim(1), transpose())

GUIDE: axis(dim(1), label("Faith_Development_Scale"))

ELEMENT: schema(position(bin.quantile.letter(Faith_Development_Scale)), label(id))

END GPL.

GGraph

Notes
Output Created / 09-OCT-2014 06:58:08
Comments
Input / Data / C:\Users\deb\Downloads\SPSS_Assignment_Data_Set(3) (1).sav
Active Dataset / DataSet1
Filter / <none>
Weight / <none>
Split File / <none>
N of Rows in Working Data File / 40
Syntax / GGRAPH
/GRAPHDATASET NAME="graphdataset" VARIABLES=Faith_Development_Scale MISSING=LISTWISE REPORTMISSING=NO
/GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
SOURCE: s=userSource(id("graphdataset"))
DATA: Faith_Development_Scale=col(source(s), name("Faith_Development_Scale"))
DATA: id=col(source(s), name("$CASENUM"), unit.category())
COORD: rect(dim(1), transpose())
GUIDE: axis(dim(1), label("Faith_Development_Scale"))
ELEMENT: schema(position(bin.quantile.letter(Faith_Development_Scale)), label(id))
END GPL.
Resources / Processor Time / 00:00:00.34
Elapsed Time / 00:00:00.34

* Chart Builder.

GGRAPH

/GRAPHDATASET NAME="graphdataset" VARIABLES=Faith_Development_Scale MISSING=LISTWISE REPORTMISSING=NO

/GRAPHSPEC SOURCE=INLINE.

BEGIN GPL

SOURCE: s=userSource(id("graphdataset"))

DATA: Faith_Development_Scale=col(source(s), name("Faith_Development_Scale"))

GUIDE: axis(dim(1), label("Faith_Development_Scale"))

GUIDE: axis(dim(2), label("Frequency"))

ELEMENT: interval(position(summary.count(bin.rect(Faith_Development_Scale))), shape.interior(shape.square))

ELEMENT: line(position(density.normal(Faith_Development_Scale)), color("Normal"))

END GPL.

GGraph

Notes
Output Created / 09-OCT-2014 06:58:44
Comments
Input / Data / C:\Users\deb\Downloads\SPSS_Assignment_Data_Set(3) (1).sav
Active Dataset / DataSet1
Filter / <none>
Weight / <none>
Split File / <none>
N of Rows in Working Data File / 40
Syntax / GGRAPH
/GRAPHDATASET NAME="graphdataset" VARIABLES=Faith_Development_Scale MISSING=LISTWISE REPORTMISSING=NO
/GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
SOURCE: s=userSource(id("graphdataset"))
DATA: Faith_Development_Scale=col(source(s), name("Faith_Development_Scale"))
GUIDE: axis(dim(1), label("Faith_Development_Scale"))
GUIDE: axis(dim(2), label("Frequency"))
ELEMENT: interval(position(summary.count(bin.rect(Faith_Development_Scale))), shape.interior(shape.square))
ELEMENT: line(position(density.normal(Faith_Development_Scale)), color("Normal"))
END GPL.
Resources / Processor Time / 00:00:00.36
Elapsed Time / 00:00:00.40