QUESTION 1

1. What is the difference between MANCOVA and ANCOVA?

2 points   

QUESTION 2

1. For questions 2 through 17, you will use the attached database to conduct a MANCOVA, including data screening and post hoc univariate ANCOVA analyses. In this study, the IV is religious affiliation (religious.affiliation), the DVs are prejudice towards “outside” religious groups (prejudice) and knowledge about “outside” religious groups (knowledge), and the covariate is exposure to “outside” religious groups (exposure). You are interested in whether religious affiliation is associated with significant differences in prejudice towards “outside” religious groups and knowledge about “outside” religious groups, when controlling for exposure to “outside” religious groups. For your first step, please develop appropriate research questions for this study. You do not have to develop null hypotheses this time. (See M & V, p. 147)

Dataset for Lab 5 _Q2-17_.sav 

3 points   

QUESTION 3

1. Screen the dataset for missing data and outliers. Are there any missing values in this dataset?

HINT: Just examine your IV, DVs, and covariate for missing data

2 points   

QUESTION 4

1. Now examine whether the DVs and the covariate have any univariate outliers. 

HINT: Since you have three continuous variables, use the z scores to establish whether you have any outliers outside of the acceptable range of -3 to +3 standard deviations. For the purposes of this quiz do not worry about multivariate outliers, but normally you should include that information in your Results write up (as in for a final exam question about MANOVA/MANCOVA you would look at Mahalnobis distance to check multivariate outliers).

2 points   

QUESTION 5

1. Examine the issue of equal split (equal n)  among the studied groups (i.e. are the groups relatively equal in their sample size?). 

2 points   

QUESTION 6

1. Now examine normality of the continuous variables (DV’s and the Covariate).  Judging by the skewness numbers for these variables, what is your conclusion about normality for these variables? (consider skewness numbers between -1 and +1 to be acceptable).

HINT: Do not use Explore option here, just use the univariate normality numbers obtained through Analyze – Descriptive Statistics – Frequencies, make sure to check the Skewness box under “Statistics” tab

2 points   

QUESTION 7

1. Now examine whether the Dependent variables and covariate meet the assumption of linearity. Then indicate which of the following is true? (HINT: Analyze – Correlate – Bivariate – put prejudice, knowledge, and exposure into the Variables box – OK).  You can look at scatterplots too if you want, that is often done to test linearity.  But for the sake of this question, which of the following is true?

2 points   

QUESTION 8

1. Conduct a preliminary MANCOVA to test the assumptions of homogeneity of variance-covariance and homogeneity of regression slopes. Then indicate which of the following statements best fits your findings. (HINT: See M & V, section 6.8 – Methods and SPSS ‘How to’ for MANCOVA; Analyze – General Linear Model – Multivariate – put prejudice and knowledge into the Dependent Variables box – put religious.affiliation into the Fixed Factors box – put exposure into the Covariates box – click Model – click Custom – then double click religious.affiliation to move it into the Model box – then double click exposure – now hold Ctrl button and single-click religious.affiliation and then exposure, highlighting them both at the same time – now click the right arrow in the middle of the screen, adding the interaction term to the pre-MANCOVA test – click Continue – click Options – move over everything from the left window into the right window – make sure that the boxes Descriptive statistics, Estimates of effect size, Homogeneity tests are checked – Continue – OK)

2 points   

QUESTION 9

1. Given your decision regarding whether the assumption of homogeneity of variance-covariance matrix was met or not, according to your book, which type of multivariate test statistic should be used? (HINT: see M & V, section 6.8/interpretation of results and figure 6.35 “Checklist for Conducting MANCOVA”)

2 points   

QUESTION 10

1. Based on your interpretation of the preliminary Custom MANCOVA, was the assumption of homogeneity of regression slopes met?

2 points   

QUESTION 11

1. Now examine the Levene’s Test of Homogeneity of Variances for this MANCOVA. Did both DVs meet this assumption?

2 points   

QUESTION 12

1. Now conduct the Full Factorial MANCOVA. Did religious affiliation have a significant main effect on the combined DV (prejudice and knowledge), when controlling for exposure?

(HINT: Analyze – General Linear Model – Multivariate – click Model – click Full factorial – Continue; Then click on Options and make sure that the boxes Compare main effects, Descriptive statistics, Estimates of effect size, and Homogeneity tests are checked, ALSO choose “Bonferroni” in the drop down menu under “Confidence Interval adjustment” – Continue – OK)

2 points   

QUESTION 13

1. Did the covariate of exposure have a significant effect on the combined DV (prejudice and knowledge)? 

2 points   

QUESTION 14

1. Did the follow-up univariate ANCOVA indicate a significant effect of the covariate exposure on any of the dependent variables individually?

2 points   

QUESTION 15

1. Did the follow-up univariate ANCOVA indicate a significant main effect of religious affiliation on knowledge of other religions?

2 points   

QUESTION 16

1. In examining the pairwise comparisons, mean scores, and looking at plots (if you wish) which of the following statements is true?

(HINT:  look at the Pairwise Comparisons table in your output, identify the significant differences [look at the Sig. column], and then examine the table with adjusted means to find the actual mean values for the significantly different religious groups)

2 points   

QUESTION 17

1. Please fill in the blanks in the following Results write-up based on information obtained in your analyses conducted in questions 2-16.

A one-way multivariate analysis of covariance (MANCOVA) was conducted to examine whether religious affiliation (IV) has a significant effect on prejudice towards “outside” religious groups (DV1) and knowledge about “outside” religious groups (DV2), when controlling for exposure to “outside” religious groups (covariate). Prior to analysis, data were examined through SPSS for accuracy of data entry, missing values, and fit between the distributions of variables and the assumptions of multivariate analysis.

 data entry errors, missing values or outliers were found in the data set. Then equality of groups on religious affiliation variable was examined. Moderate split was found among groups with different denominations (Catholic n = ; fundamentalist n = ; LDS church n = , Jewish n = , Episcopal n = ). Next, univariate normality of prejudice, knowledge, and exposure variables was examined. Skewness of all three variables were within normal limits (prejudice skewness = , knowledge skewness = , exposure skewness = ); thus, these variables were assumed to have normal distributions, and no transformations were necessary.

Next, assumption of linearity between the dependent variables and the covariate was examined through scatter plots and bivariate correlations. All three correlations were significant, and Pearson coefficients were moderate to high for all three correlations (prejudice*exposure r = , p = ; knowledge*exposure r = , p =; prejudice*knowledge r = , p < ), which indicated linear relationships among these three variables.

Further, a test of homogeneity of variance-covariance matrices was conducted. Box’s test of equality of covariance matrices revealed that the assumption of homogeneity of variance-covariance was  (Box’s M = , F(, ) = , p < ). This finding, combined with unequal n problem, indicated that  needed to be utilized as the test statistic for all the multivariate tests. A subsequent test of homogeneity of regression slopes revealed that factor-covariate interaction was  (Pillai’s Trace = ; F(, ) = , p = ), and therefore further analysis was acceptable. Finally, within preliminary MANCOVA homogeneity of variance was also examined. Levene’s Test of Equality of Variances was  for prejudice, but it was  for knowledge, indicating that the assumption of homogeneity of variances was met for knowledge, but not for prejudice.

Finally, a one-way MANCOVA was conducted. Results of MANCOVA revealed that religious affiliation had a significant main effect on the combined DV (prejudice and knowledge), when controlling for exposure (Pillai’s Trace = , F(, ) = , p < , multivariate η² = ), but the covariate of exposure did not significantly affect the combined dependent variable (Pillai’s Trace = , F(, ) = , p = , multivariate η² = ).

Analyses of covariance (ANCOVA) were conducted for each dependent variable as follow up tests for MANCOVA. Follow up ANCOVA tests indicated that the covariate of exposure did not have a significant effect on either one of the dependent variables individually (prejudice, F(, ) =, p = , partial η²  = ; knowledge F(, ) = , p = , partial η² = ).  However, religious affiliation  affected both dependent variables individually (prejudice F(, ) = , p < .001, partial η² = ; knowledge F(, ) = , p < .001, partial η² = ), when controlling for exposure to “outside” religious groups.

Next, Bonferroni pairwise comparisons were conducted to further explore which religious groups had significantly different prejudice and knowledge scores. Pairwise comparisons revealed that after adjusting for exposure to outside religions, participants who identified themselves as Catholics (prejudice adjusted M = ) were significantly more prejudiced against outside religious groups, compared to the prejudice level for the Episcopal (prejudice adjusted M = ) and the Jewish (prejudice adjusted M = ) participants.  Participants who identified themselves as Fundamentalists (prejudice adjusted M = ) received the highest scores on the measure of prejudice, and they were significantly more prejudiced against outside religious groups, compared to the prejudice level for the Episcopal and the Jewish respondents.  Further, participants with the Catholic affiliation received lowest scores on the measure of knowledge of outside religions (knowledge adjusted M = ), and their scores were significantly lower than knowledge scores of all other religious groups. The group with the next lowest knowledge score, Fundamentalist group (knowledge adjusted M= ), was significantly less knowledgeable about outside religions than the Jewish group (knowledge adjusted M = ) and the Episcopal group (knowledge adjusted M = ). 

Overall, results of this study suggest that religious affiliation significantly affects prejudice towards and knowledge about “outside” religious groups, when these variables are considered both together and individually, and when the effect of exposure to “outside” religious groups is controlled for.  In fact, when controlling for exposure, religious affiliation accounts for % of the variance in the combined “knowledge and prejudice” variable, % of variance on the prejudice variable individually, and % of variance on knowledge individually.

72 points   

QUESTION 18

1. Create an APA-style table of adjusted and unadjusted means for the MANCOVA that you wrote up in the previous question 

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