SPSS ANOVA & MANOVA Assignment

SPSS ANOVA & MANOVA 1

Deborah Davis

Liberty University

The purpose of this document is to provide a response to the fourth SPSS assignment that covers the use and understanding of the ANOVA and MANOVA test programs 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. 2).

Structure

In that there are two research questions 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 i will be separated within each aspect.

Research Question 1

Is there a statistically significant relationship[AJR1] between students’ total sense of community as measured by the Classroom Community Scale (CCS, Rovai, 2002) based on the type of three different mediums (video conferencing, chat systems, and Blackboard discussion forums)they used for class discussions in an online statistics course?

Null Hypothesis

There is no significant relationship between students’ total sense of community as measured by the Classroom Community Scale (CCS, Rovai, 2002) based on the type of three different mediums (video conferencing, chat systems, and Blackboard discussion forums) they used for class discussions in an online statistics course.

Alternative Hypothesis 1[AJR2]

There is asignificant relationship between students’ total sense of community as measured by the Classroom Community Scale (CCS, Rovai, 2002) based on the use of video conferencing as opposed to chat systems or Blackboard discussion board forums when used for class discussions in an online statistics course.

Alternative Hypothesis 2

There is asignificant relationship between students’ total sense of community as measured by the Classroom Community Scale (CCS, Rovai, 2002) based on the use of chat systems as opposed to video conferencing or Blackboard discussion board forums when used for class discussions in an online statistics course.

Alternative Hypothesis 3

There is a significant relationship between students’ total sense of community as measured by the Classroom Community Scale (CCS, Rovai, 2002) based on the use of Blackboard discussion board forums as opposed to chat systems or video conferencing when used for class discussions in an online statistics course.

Independent Variables – Communication Medium

Blackboard Discussion Board forums (1)

Chat systems (2)

Video conferencing (3)

All are nominally measured as there is no actual measure nor score nor rating in the three systems.

Dependent Variables – Community Connectedness Scale

Students’ total community score as measured by the Classroom Community Scale (Rovai, 2002)

This is an interval/ratio measure as it contains a score which can be measured and can contain any numeral including zero.

Test to be Used

Since there is one dependent variable that is continuous and an independent variable with three independent levels, the appropriate test for statistical significance would be a one- way between groups ANOVA[AJR3]. The term one-way indicates that there is only one independent variable while between groups indicates multiple groups within the dependent variable (Szapkiw, 2012). A non-parametric alternative would be the Kruskal-Wallis test (Green & Salkind, 2008, p. 393) as it would evaluate the medians on a dependent variable across all levels of the factor. A paired sample t-test would examine the difference between two paired scores, not relationship, thus it is also ruled out of consideration.

Assumptions[AJR4]

Preliminary analyses using a scatter plot were performed to ensure no violations of the assumptions of linearity, normality, and homoscedasticity; assumptions were found tenable. 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. A paired sample t test examines the difference between two paired scores, not relationship.

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, standard deviation, and group number for community connectedness was performed against discussion board (M = 18.43, SD = 5.72, n = 14), chat systems (M = 25.42, SD = 8.67, n = 12) and video conferencing (M = 37.00, SD = 1.92, n = 14) and then against the whole population (M = 27.03, SD = 9.82, N=40[AJR5]). See Table 1.

Table 1.

Descriptive Statistics for Community Connectedness and Methods of Communication (N = 40)

Group / n / M / SD
Discussion Board / 1 / 14 / 18.43 / 5.72
Chat / 2 / 12 / 25.42 / 8.67
Video Conferencing / 3 / 14 / 37.00 / 1.92
Total / 40 / 27.03 / 9.82

Results

The tests reflect that it is appropriate to reject the null hypothesis: There is not a significant difference between students’ total sense of community as measured by the Classroom Community Scale (CCS, Rovai, 2002) based on the type of medium (video conferencing, chat systems, or Blackboard discussion boards) used for class discussions in the online Introduction to Statistics course. Tests also reflect that Alternative Hypothesis 1 is valid: There is a significant difference between students’ total sense of community as measured by the Classroom Community Scale (CCS, Rovai, 2002) based on the use of video conferencing as opposed to chat systems or Blackboard discussion boards when used for class discussions in the online Introduction to Statistics course.

Partial correlatio[AJR6]n was used to evaluate the null hypothesis:There is no significant relationship between students’ total sense of community as measured by the Classroom Community Scale (CCS, Rovai, 2002) based on the type of three different mediums (video conferencing, chat systems, and Blackboard discussion forums) they used for class discussions in an online statistics course. The assumption of homogeneity of variance was tested and found not tenable using Levene’s test for community connectednessF(2, 37) = 14.54, p = 0.00. Since the significance value of 0.00 is less than 0.05 and thus violates the assumption of homogeneity of variance, the assumption is not tenable therefore a robust test of equality of means was consulted.

The[AJR7] robust test of equality of means was used providing results of both Welch F(2, 27.97) = 70.90, p = 0.00, and Brown-Forsythe F(2, 20.28) = 32.23, p = 0.00[AJR8]. This also reflected a significance value of 0.00 but suggests the post hoc equal variances not assumed test (e. g. Games-Howel[AJR9]l) would be more valid due to the small n’s and the inequality between them. See Table 2.

Table 2

Robust Tests of Equality of Means
Community_Connectedness_Scale
Statistica / df1 / df2 / Sig.
Welch / 70.900 / 2 / 17.968 / .000
Brown-Forsythe / 32.226 / 2 / 20.282 / .000
a. Asymptotically F distributed.

A review of the ANOVA F (2, 39) = 34.98, p = 0.00[AJR10] reflects a significance of 0.00. Since this is less than 0.05, we know that there is a statistically significant result somewhere in the groups.

Since our overall ANOVA was significant, we [AJR11]now review the multiple comparisons table. This would not be needed were the overall ANOVA not significant. Box’s Test of Equality of Covariance Matrices F(6, 29158.60) = 6.43, p = .000[AJR12] reflecting, again, a significance of less than .05. Tests revealed significant pairwise differences between the mean scores of community connectedness for those who participated via video conferencing and both students communicating via discussion forums and chat systems, p < .05. Students who communicated via discussion forums and chat systems reflected no significant difference in community connectedness. [AJR13][AJR14]

Thus a comparison of the mean scores between the groups as reflected in the means plot appears dramatic, but a review of the means in the descriptive table reflects a less dramatic variance. See Figure 2.

Figure 2.

Effect Size

The effect size was computed using eta squared. The formula for eta squared is the sum of squares between groups divided by the total sum of squares. In this case, that would be 2456.63 divided by 3758.98 giving an eta squared value of 0.65 which is then evaluated based on Cohen (1988) as a standard. Using the Suggested Verbal Labels for Cohen’s d indicates this to be a large effect[AJR15].

Post Hoc

Post hoc comparisons to evaluate pairwise difference among group means were conducted with the use of Tukey HSD test through equal variances were found untenable. Tests revealed significant pairwise differences between the mean scores of students who used video conferencing and students who used either discussion board or chat systems, p < .05. Students who used discussion board and chat systems did not significantly differ from each other.

Research Question 2

Is there a statistically significant difference in students’ total sense of community as measured by the Classroom Community Scale (CCS, Rovai, 2002) and perceived learning as measured by the Perceived CAP Learning Scale (Rovai et al. 2009) based on the type of medium (video conferencing, chat systems, or Blackboard discussion boards) used for class discussions in the online Introduction to Statistics course?

Null Hypothesis

There is not a significant difference between students’ total sense of community as measured by the Classroom Community Scale (CCS, Rovai, 2002) and perceived learning as measured by the Perceived CAP Learning Scale (Rovai et al. 2009) based on the type of medium (video conferencing, chat systems, or Blackboard discussion boards) used for class discussions in the online Introduction to Statistics course[AJR16].

Alternative Hypothesis 1

There is a significantdifference between students’ total sense of community as measured by the Classroom Community Scale (CCS, Rovai, 2002) and perceived learning as measured by the Perceived CAP Learning Scale (Rovai et al. 2009) based on the use of video conferencing as opposed to chat systems or Blackboard discussion boards when used for class discussions in the online Introduction to Statistics course.

Alternative Hypothesis 2

There is a significant difference between students’ total sense of community as measured by the Classroom Community Scale (CCS, Rovai, 2002) and perceived learning as measured by the Perceived CAP Learning Scale (Rovai et al. 2009) based on the use of chat systems as opposed to video conferencing or Blackboard discussion boards when used for class discussions in the online Introduction to Statistics course.

Alternative Hypothesis 3

There is a significant difference between students’ total sense of community as measured by the Classroom Community Scale (CCS, Rovai, 2002) and perceived learning as measured by the Perceived CAP Learning Scale (Rovai et al. 2009) based on the use of Blackboard discussion boards as opposed to chat systems or video conferencing when used for class discussions in the online Introduction to Statistics course.

Independent Variables – Communication Medium

Blackboard Discussion Board forums (1)

Chat systems (2)

Video conferencing (3)

All are nominally measured as there is no actual measure nor score nor rating in the three systems.

Dependent Variables

Sense of community as measured by the Classroom Community Scale (CCS, Rovai, 2002)

Perceived learning as measured by the Perceived CAP Learning Scale (Rovai et al. 2009)

Both are interval/ratio measures as both contain a score which can be measured and can contain any numeral including zero[AJR17].

Test to be Used

Since there aretwodependent[AJR18] variables that are continuous and an independent variable with three independent levels, the appropriate test for statistical significance is twoone[AJR19]-way MANOVA(Warner, 2008, p. 702).

Assumptions

The dependent variables(sense of community and perceived learning) aremeasured at the interval or ratio level. The independent variables (communications medium) consist of three categorical independent groups (discussion board, chat, and video). There is independence of observations as those in each of the discussion medium groups are in a singular group only. There should be no significant outliers, which the two-way MANOVA will detect. The dependent variable should be approximately normally distributed for each combination of the groups of the independent variables which will be tested using Shapiro-Wilkes. There needs to be homogeneity of variances for each combination of the groups of the two independent variables which will be tested using Levene’s test.

Figure 2

Descriptive Statistics

This assignment required elements to be presented from the data set provided. An SPSS analysis of the mean, standard deviation, for community connectedness[AJR21](M = 27.03, SD = 9.82, N = 40) for discussion board (M = 18.43, SD = 5.72, n = 14), chat systems (M = 25.42, SD = 8.67, n = 12) and video conferencing (M = 37.00, SD = 1.92, n = 14). The same analysis was performed on perceived learning (M = 37.43, SD = 13.86, N = 40) for discussion board (M = 26.07, SD = 9.18, n = 14), chat systems (M = 35.25, SD = 13.41, n = 12) and video conferencing (M = 50.64, SD = 2.95, n = 14). See Table 2.

Table 2.

Descriptive Statistics for Community Connectedness and Perceived Learning Scale (N = 40)

Group / n / M / SD
Community Connectedness / Discussion Board / 14 / 18.43 / 5.72
Community Connectedness / Chat / 12 / 25.42 / 8.67
Community Connectedness / Video Conference / 14 / 37.00 / 1.92
Community Connectedness / Total / 40 / 27.03 / 9.82
Perceived Learning Scale / Discussion Board / 14 / 26.07 / 9.19
Perceived Learning Scale / Chat / 12 / 35.25 / 13.41
Perceived Learning Scale / Video Conference / 14 / 50.64 / 2.95
Perceived Learning Scale / Total / 40 / 37.43 / 13.86

Table 1

Dependent Variable Descriptive Statistics Disaggregated by the Independent Variable (N = 40)

Discussion Board
( n = 14) / Chat
( n = 12) / Video Conferencing
( n = 14)
Variable / M / SD / M / SD / M / SD
Learning / 26.07 / 9.19 / 35.25 / 13.41 / 50.64 / 2.95
Community / 36.93 / 11.69 / 52.83 / 17.78 / 73.93 / 3.71

Results

The tests reflect that it is appropriate to reject the null hypothesis:[AJR22] There is not a[AJR23] significant difference between students’ total sense of community as measured by the Classroom Community Scale (CCS, Rovai, 2002) and perceived learning as measured by the Perceived CAP Learning Scale (Rovai et al. 2009) based on the type of medium (video conferencing, chat systems, or Blackboard discussion boards) used for class discussions in the online Introduction to Statistics course. Tests also reflect that Alternative Hypothesis 1 is valid: There is a significant difference between students’ total sense of community as measured by the Classroom Community Scale (CCS, Rovai, 2002) and perceived learning as measured by the Perceived CAP Learning Scale (Rovai et al. 2009) based on the use of video conferencing as opposed to chat systems or Blackboard discussion boards when used for class discussions in the online Introduction to Statistics course.

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. The Levene’s test shows an error variance of the dependent variable for community connectedness F(2, 37) = 0.00,p = 14.54 and for perceived learning F (2, 37) = 0.00, p = 10.57. This reflects that the assumption of homogeneity of variance (as p<.05) has been violated and a more robust measure is required. The results of the ANOVA[AJR24] indicated a significant affect among the groups for communication medium, Wilks’ Lambda[AJR25] = .33, F = (4, 72) = 13.21, p < .01, ∂2 =.42. Therewas significant evidence to reject the null hypothesis and conclude that there was a statistically significant relationship between the type of communication medium used and both the sense of community and perceived learning. Video conferencing had significantly higher levels of both perceived learning andhigher levels of community[AJR26].

Effect Size

The effect size was determined using the formula for Wilks’ Lambda for partial Eta SquaredF (4, 72) = 13.21, p <.01, ᾐ2 = .42. This, as reflected in Cohen (1988) would indicate a strong effect for this relationship.

Post Hoc

Post hoc comparisons to evaluate pairwise difference among group means were conducted with the use of Tukey HSD test and Games-Howell though equal variances were found untenable[AJR27]. Tests revealed significant pairwise differences between the mean scores of students who used video conferencing and students who used either discussion board or chat systems, p < .05. Students who used discussion board and chat systems did not significantly differ from each other. [AJR28]

References

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

Green, S. B., & Salkind, N. J. (2008). Using SPSS for Window and Macintosh: Analyzing andunderstanding data (5th ed.). Upper Saddle River, NJ: Pearson Prentice Hall.

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), 7-13.

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

Appendix

ONE WAY ANOVA

GET

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

DATASET NAME DataSet1 WINDOW=FRONT.

* Chart Builder.

GGRAPH

/GRAPHDATASET NAME="graphdataset" VARIABLES=Community_Connectedness_Scale Communication_Medium MISSING=LISTWISE REPORTMISSING=NO

/GRAPHSPEC SOURCE=INLINE.

BEGIN GPL

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

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

DATA: Communication_Medium=col(source(s), name("Communication_Medium"), unit.category())

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

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

SCALE: cat(dim(2), include("1", "2", "3"))

ELEMENT: point(position(Community_Connectedness_Scale*Communication_Medium))

END GPL.

GGraph

Notes
Output Created / 26-FEB-2014 11:57:18
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 / GGRAPH
/GRAPHDATASET NAME="graphdataset" VARIABLES=Community_Connectedness_Scale Communication_Medium MISSING=LISTWISE REPORTMISSING=NO
/GRAPHSPEC SOURCE=INLINE.
BEGIN GPL
SOURCE: s=userSource(id("graphdataset"))
DATA: Community_Connectedness_Scale=col(source(s), name("Community_Connectedness_Scale"))
DATA: Communication_Medium=col(source(s), name("Communication_Medium"), unit.category())
GUIDE: axis(dim(1), label("Community_Connectedness_Scale"))
GUIDE: axis(dim(2), label("Communication_Medium"))
SCALE: cat(dim(2), include("1", "2", "3"))
ELEMENT: point(position(Community_Connectedness_Scale*Communication_Medium))
END GPL.
Resources / Processor Time / 00:00:02.14
Elapsed Time / 00:00:02.90

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

ONEWAY Community_Connectedness_Scale BY Communication_Medium

/STATISTICS DESCRIPTIVES HOMOGENEITY BROWNFORSYTHE WELCH

/PLOT MEANS

/MISSING ANALYSIS

/POSTHOC=TUKEY ALPHA(0.05).

Oneway

Notes
Output Created / 26-FEB-2014 12:00:48
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 for each analysis are based on cases with no missing data for any variable in the analysis.
Syntax / ONEWAY Community_Connectedness_Scale BY Communication_Medium
/STATISTICS DESCRIPTIVES HOMOGENEITY BROWNFORSYTHE WELCH
/PLOT MEANS
/MISSING ANALYSIS
/POSTHOC=TUKEY ALPHA(0.05).
Resources / Processor Time / 00:00:00.37
Elapsed Time / 00:00:00.63

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