Answers for Assignment #4

3a. Two-way MANOVA

A 2X2 MANOVA was conducted to examine the difference in students gender and parent's marital status on the students' academic performance. The dependent variables were 3rd grade reading and math scores. The independent variables are student gender (female and male) and parents' marital status (divorced or married). The means and standard deviations by gender and marital status are reported below. The assumption of equality of covariance matrices was satisfied, Box's M=3.75, F=.41, p=.93. There was a significant main effect for gender (Wilks' Lambda=.964, F=13.89, p<.001, eta squared=.036), but not a significant main effect for marital status (Wilks' Lambda=.99, F=2.44, p=.088, eta squared=.007) or the interaction between gender or martial status (Wilks' Lambda=.99, F=.60, p=.549, eta squared=.002). To further examine the differences between the genders, univariate follow-up procedures were conducted to determine differences in the individual dependent variables. The results indicated that there was a statistically significant difference in the mean reading score (F=21.302, p<.001), with females scoring higher on average. There was no significant different in the math mean scores (F=1.829, p=.177).

 

 3c. A write-up

Results

             A 2X3 between subjects multivariate analysis of variance was performed on three dependent variables: Verbal SAT, Mathematic SAT, and GPA. Independent variables were gender and race (white, African American, and other). No datum is missing on any of the dependent variables. The sample sizes are quite different in the six groups. The sample sizes for the groups are reported in Table 1. There were very little differences in variance and the discrepancies, and none of the largest to smallest variance approach 10:1. Box’s M test for homogeneity of dispersion matrices found significant differences (Box’s M=69.2, F=2.3, p<.001). Pillai’s criterion will be used to evaluate the multivariate statistics. Results of the evaluation of assumptions of normality, linearity, and multicollinearity were satisfied.

Table 1

Sample Sizes for Groups

 

White

Af Amer

Other

Total

Females

621

188

54

863

Males

509

76

52

637

Total

1130

264

106

1500

     The means and standard deviations for the three dependent variables by gender and race are reported in Table 2. With the use of Pillai’s criterion, the combined DVs were significantly affected by gender, F(3, 1492)=14.66, p<.001, and race F(6, 2984)=44.72, p<.001, and by their interaction, F(6, 2984)=2.68, p<.05. The results reflected a modest association between race (partial η2 of .08) and the combined DVs. The association was less substantial for gender (partial η2 of .03) and the interaction of gender and race (partial η2 of .005).

Table 2

Means and Standard Deviations for SAT Verbal and Math and GPA

 

 

Female

 

Male

 

Total

SAT Verbal

M

SD

 

M

SD

 

M

SD

white

514.32

72.50

 

528.88

76.16

 

520.88

74.49

Afr-am

458.67

77.59

 

468.68

71.65

 

461.55

75.93

other

470.74

88.04

 

438.65

93.35

 

455.00

91.67

Total

499.47

78.34

 

514.33

82.61

 

505.78

80.49

SAT Math

 

 

 

 

 

 

 

 

white

508.39

69.46

 

545.44

73.88

 

525.08

73.80

Afr-am

439.36

67.61

 

469.74

72.64

 

448.11

70.32

other

498.52

64.09

 

524.04

73.57

 

511.04

69.76

Total

492.73

74.26

 

534.66

77.60

 

510.54

78.46

GPA

 

 

 

 

 

 

 

 

white

2.52

0.88

 

2.32

0.95

 

2.43

0.92

Afr-am

2.29

0.80

 

2.16

0.78

 

2.25

0.79

other

2.22

1.01

 

2.34

0.67

 

2.28

0.86

Total

2.45

0.88

 

2.30

0.91

 

2.39

0.89

     Univariate tests were used to examine differences between gender and race for each DV, and the results are reported in Table 3. There was a significant difference between genders on SAT math (F=28.75, p<.01), with males scoring higher than females. For race, there were statistically significant differences for all three dependent variables. Scheffe post hoc procedures were used to determine significant differences between whites, African Americans, and others.  On the SAT verbal, whites had a significantly higher means than both African Americans and others. On the SAT math, both whites and others had higher mean scores than African Americans. Whites had a higher mean GPA than African Americans. There was a statistically significant interaction of the two IVs and SAT verbal. An illustration of the interaction is illustrated in Figure 1. White and African American males tend to score higher on the SAT verbal, but in the ethnic group other the females tended to score higher.

Table 3

Univariate Results for the Three DVs

Factor

DVs

F

p

η2

Gender

SAT-V

.16

.69

.00

 

SAT-M

28.75

.00

.02

 

GPA

.92

.34

.00

 

 

 

 

 

Race

SAT-V

81.33

.00

.10

 

SAT-M

94.65

.00

.11

 

GPA

5.03

.01

.01

 

 

 

 

 

Gender*Race

SAT-V

4.59

.01

.01

 

SAT-M

.47

.63

.00

 

GPA

1.72

.18

.00

 

 

 Figure 1. The gender by race interaction of the SAT verbal.