Answer Key Chapter 2 1. Bivariate regression 2. One-way MANOVA 3. T-test of independent samples 4. Bivariate correlation 5. Discriminant Analysis 6. One-way ANCOVA 7. One-way MANCOVA 8. Multiple regression 9. One-way ANOVA 10. Two-way MANOVA 11. Logistic regression 12. Two-way ANOVA 13. Factor Analysis Chapter 3 Output for Exercise 3.1.
1a. There are no missing values for either variable. 1b. Peduc2 has a large split in that n=121 (77%) with a master’s degree and n=36 (23%) with a postmaster’s degree. However, it is not extreme (90/10). 1c. Boxplots identify two outliers (cases 38 and 40) for the post-master’s group in Humility. 1d. Normality may be assumed as tests of normality are not significant. No transformation is necessary. 1e. Homogeneity of variances is not assumed since Levene’s is significant (p = .021) 1f. Remove the outliers for the post-master’s group, where HumilityMean < 3.0. This may improve homoscedasticity. The authors did NOT conduct this transformation.
Output for Exercise 3.2.
2a. There are no missing data. The box plots do not identify an outliers. However, since normality is violated for HumilityMean and MLQMean, we will examine the histograms to identify extreme values. Histograms do not reveal extreme outliers. No transformations will be made at this time. 2b. Chi-square criteria for three quantitative variables (df = 3) at p = .001 is 2 = 16.266. The box plot of multivariate outliers for Mahalanobis distance identifies two values that exceed 16.266. Use select cases. 2c. Scatter plot matrix indicates no curvilineary. Linearity will be assumed. Plots are fairly elliptical. Normality will be assumed. 2d. Residuals plot shows not extreme clustering. Homoscedasticity will be assumed.
Chapter 4 Output for Exercise 4.1
1a. RQ1: Does principal gender and level of education significantly interact on Self-Awareness? RQ2: Is there a difference in Self-Awareness between female and male principals? RQ3: Is there a difference in Self-Awareness between principals with a master’s degree and postmaster’s degree? 1b. The line plot shows no interaction. 1c. Males score higher than females, but it may not be significant. 1d. Post-masters score higher than Master’s. The difference is sizable and is likely significant. Output for Exercise 4.2
2a. Homegeneity of variances is assumed. 2b. Interaction is not significant; F(1,153) = 0.35, p =.555, partial 2 = .002. 2c. The main effect of gender is not significant; F(1,153) = 3.12, p =.08, partial 2 = .020. The main effect of education level is significant; F(1,153) = 18.16, p < .001, partial 2 = .106. Principals with a post-master’s degree score significantly higher is Self-Awareness. 2d. Results are likely fairly similar to estimation. 3. Factorial ANOVA was conducted to examine the interaction between principal gender and level of education on Self-Awareness. Of the 157 principals evaluated, 63 (40%) were female, while 121 (77%) had a master’s degree. Descriptive statistics are presented in Table 1. ANOVA results (see Table 2) indicate that interaction between gender and education level on Self-awareness is not significant; F(1,153) = 0.35, p =.555, partial 2 = .002. Although males scored higher than females in Self-awareness, the main effect of gender was not significant; F(1,153) = 3.12, p =.08, partial 2 = .020. The main effect of education level is significant where principals with a post-master’s degree score significantly higher in Self-Awareness.; F(1,153) = 18.16, p < .001, partial 2 = .106. Table 1. Descriptive Statistics for Principal Self-awareness by Gender and Education Level
Master’s Post-Masters
n 43 20
Female M 3.00 3.64
SD .99 .80
Male M 3.13 3.82
n 78 16
SD .94 .75
Table 2. Two-way ANOVA Summary Table Source
SS
df
MS
F
p
Partial 2
Between treatments
48.40
3
16.13
23.70
<.001
.320
Gender
4.40
1
4.40
6.46
.012
.041
Education
26.28
1
26.28
38.61
< .001
.204
Gender x Education
2.84
1
2.84
4.18
.043
.027
Within treatments
102.78
151
0.68
Total
2098.55
155