# Module 6 – General Linear Models: ANOVA & ANCOVA

August 30, 2017

Question
Module 6 – General Linear Models: ANOVA & ANCOVA

The two exercises below utilize the data sets career-a.sav and career-f.sav, which can be downloaded from this Web site:
.pyrczak.com/data”>www.Pyrczak.com/data
1. You are interested in evaluating the effect of job satisfaction (satjob2) and age category (agecat4) on the combined DV of hours worked per week (hrsl) and years of education (educ). Use career-a.sav for steps a and b.
a. Develop the appropriate research questions and/or hypotheses for main effects and interaction.
b. Screen data for missing data and outliers. What steps, if any, are necessary for reducing missing data and outliers?
For all subsequent analyses in Question 1, use career-f.sav and the transformed variables of hrs2 and educ 2.
c. Test the assumptions of normality and linearity of DVs.
i. What steps, if any, are necessary for increasing normality?
ii. Are DVs linearly related?

d. Conduct MANOVA with post hoc (be sure to test for homogeneity of variance-covariance).
a. Can you conclude homogeneity of variance-covariance? Which test statistic is most ap¬propriate for interpretation of multivariate results?
b. Is factor interaction significant? Explain.
c. Are main effects significant? Explain.
d. What can you conclude from univariate ANOVA and post hoc results?
e. Write a results statement.
2. Building on the previous problem, in which you investigated the effects of job satisfaction (satjobl) and age category (agecat4) on the combined dependent variable of hours worked per week (hrsl) and years of education (educ), you are now interested in controlling for respondents’ income such that rin- com91 will be used as a covariate. Complete the following using career-a.sav.
i. Develop the appropriate research questions and/or hypotheses for main effects and interaction.
ii. Screen data for missing data and outliers. What steps, if any, are necessary for reducing missing data and outliers?
For all subsequent analyses in Question 2, use career-f.sav and the transformed variables of hrs2, educ2, and rincoml.
iii. Test the assumptions of normality and linearity of DVs and covariate.
i. What steps, if any, are necessary for increasing normality?
ii. Are DVs and covariate linearly related?

c. Conduct a preliminary MANCOVA to test the assumptions of homogeneity of variance- covariance and homogeneity of regression slopes/planes.
i. Can you conclude homogeneity of variance-covariance? Which test statistic is most appropriate for interpretation of multivariate results?
ii. Do factors and covariate significantly interact? Explain.
d. Conduct MANCOVA.
i. Is factor interaction significant? Explain.
ii. Are main effects significant? Explain.
iii. What can you conclude from univariate ANOVA results?
e. Write a results statement.
3. Compare the results from Question 1 and Question 2. Explain the differences in main effects.

The following output was generated from conducting a forward multiple regression to identify which IVs {urban, birthrat, Inphone, and Inradio) predict Ingdp. The data analyzed were from the SPSS country-a.sav data file.
Variables Entered/Removed 1
Variables Variables
Model Entered Removed Method
1 Forward
(Criterion:
LNPHONE Probability
y-of-F-to-e
nter <=
.050)
2 Forward
(Criterion:
BIRTHRAT Probability
y-of-F-to-e
nter www.Pvrczak.com/data

You are interested in examining whether the variables shown here in brackets [years of age (age), hours worked per week (hrsl), years of education (educ), years of education for mother (maeduc), and years of education for father (paeduc)] are predictors of individual income (rincmdol). Complete the following steps to conduct this analysis.
a. Using profile-a.sav, conduct a preliminary regression to calculate Mahalanobis distance. Iden¬tify the critical value for chi-square. Conduct Explore to identify outliers. Which cases should be removed from further analysis?
For all subsequent analyses, use profile-b.saw Make sure that only cases where MAH l [Jwidth “{“Decimals] Label Values Missin g ] Columns E Align Measure T~ Role
1 salary Numeric 8 2 None None 8 9 Right f Scale S Input
2 yos Numeric 8 2 None None 8 m Right # Scale \ Input
3 sex Numeric 8 2 (1 00. Male) None 8 m Right Nominal \ Input
4 classify Numeric 8 2 {1 00, Cleric None 8 9 Right A Nominal \ Input
5 educ Numeric 8 2 None None 8 9 Right f Scale \ Input

SALARY YOS SEX CLASSIFY EDUC
35,000 8 Male Technical 14
18,000 4 Female Clerical 10
20,000 1 Male Professional 16
50,000 20 Female Professional 16
38,000 6 Male Professional 20
20,000 6 Female Clerical 12
75,000 17 Male Professional 20
40,000 4 Female Technical 12
30,000 8 Male Technical 14
22,000 15 Female Clerical 12
23,000 16 Male Clerical 12
45,000 2 Female Professional 16

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