1. Intermediate Statistics Final Exam
Michael Parent
Question 1
This two-way ANOVA estimates the impact of the main effects of grade level and gender has on
the dependent variable "out of school I play (hangout with friends)".
In reviewing the Tests of Between-Subject Effects, I wanted to determine Are the main effects
significant?
• The main effect of grade level is significant with a significance level of .043, degrees of
freedom of 1, 116, and an F-value of 4.191.
• The main effect of gender is not significant with a significance level of .343, degrees of
freedom of 1, 116, and an F-value of .908.
• The interaction effect of grade level and gender is significant with a significance level
of .024, degrees of freedom of 1, 116, and an F-value of 5.251.
Thus, the main effect of gender is not a significant predictor of the degree to which students
report that “out of school I play”. The main effect of grade level and the main effect of grade
level combined with the main effect of gender is a significant predictor of the degree to which
students report that “out of school I play"
In reviewing the Estimated Marginal Means, I wanted to determine Is there a difference in “out
of school I play” for the main effects that were significant? The first main effect that was
significant was grade level. The means of grade levels are as follows:
• Fourth grade – mean score of 3.296 and a standard error of .099
• Fifth grade – mean score of 3.575 and a standard error of .094
There is a .279 difference between the mean scores with 5th graders scoring higher. This
means that 5th graders report that out of school they play out of school to a greater degree than
4th graders.
Table two of the Estimated Marginal Means indicates that for the main effect of Gender:
• Males have a mean score of 3.501 with a standard error of .095.
• Females have a mean score of 3.370 with a standard error of .098.
There is a .131 difference between the mean scores with males scoring higher. This means that
males report that out of school they play to a greater degree than females.
Table three of the Estimated Marginal Means indicates the interaction between grade level and
student gender. The means of the grade level and student gender are as follows:
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2. Intermediate Statistics Final Exam
Michael Parent
• Males Fourth grade – mean score of 3.517 and a standard error of .137
• Females Fourth grade – mean score of 3.074 and a standard error of .142
There is a .443 difference between the mean scores with 4th grade males scoring higher. This
means that 4th grade males report that Out of school they play (hang out with friends) to a a
greater degree than 4th grade females
• Males Fifth grade – mean of 3.484 and a standard error of .133
• Females Fifth grade – mean of 3.667 and a standard error of .135
There is a .183 difference between the mean scores with 5th grade females scoring higher. This
means that 5th grade females report that out of school they play to a greater degree that 5th
grade males.
A review of the Profile Plots indicates that there is a disordinal relationship/interaction between
females and males. In the fourth grade, males report a greater degree "out of school I play" to
than do females. On the profile plot, the lines for males and females intersect when males and
female students are nearly entering the 5th grade. Beginning in the fifth grade, females report
"out of school I play" to a greater degree than males.
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3. Intermediate Statistics Final Exam
Michael Parent
Question 2
This analysis of Covariance (ANCOVA) aims to determine the impact of the main effects of
student gender and grade level on the dependent variable "Out of School I play (hang out with
friends)" after controlling for the co-variate "Out of school I play organized sports".
In reviewing the Tests of Between-Subject Effects, I wanted to determine Are the main effects
significant? This table indicates that the corrected model is significant at .002 level, with an F
value of 4.432, df:4,105. The table also indicates:
• Ques6b is significant with a significance level of .002, degrees of freedom 1, 105, and
an F-value of 10.368
• Student gender is not significant with a significance level of .714, degrees of freedom
1,105, and an F-value of .135
• Grade level is not significant with a significance level of .063, degrees of freedom 1,
105, and an F-value of 3.522,
• Gender and Grade level is significant with a significance level of .050, degrees of
freedom1,105, and an F-value of 3.939
The covariate Ques6B is significant at .002 level. This means that there are differences between
genders. However, after controlling for Ques6b, Gender is not a significant predictor for
reporting patterns regarding the independent variable "Out of school I play (hang out with
friends)".
In reviewing the Estimated Marginal Means, the mean score for the main effect of Student
Gender are as follows:
• Males – a mean score of 3.408 with a standard error of .097
• Females – a mean score of 3.461 with a standard error of .101
There is a difference of .004 between the means with the mean score for females being higher.
This indicates that females tend to report that "Out of school I play (hang out with friends)" to a
greater degree after controlling preexisting differences between males and females,
represented by the co-variate "Out of school I play organized sports".
A review of the Profile Plots indicates a dis-ordinal relationship between females and males.
After controlling for "Out of school I play organized sports" (Ques6B), the dis-ordinal interaction
is similar. In fourth grade, males report "after school I play (hangout with friends)” to a greater
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4. Intermediate Statistics Final Exam
Michael Parent
degree than females. Prior to entering the fifth grade there is a reversal; females begin reporting
"after school I play (hangout with friends) to a greater degree than males. The relationship
between males and females reporting “out of school I play” is dis-ordinal for the ANCOVA just
as it was dis-ordinal in the Two-Way ANOVA.
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5. Intermediate Statistics Final Exam
Michael Parent
Questions 3
This is a hierarchical regression that has three models. The first model shows the impact of
student gender on overall academic performance. The second model shows the impact of
attendance in class on overall academic performance. The third model shows the impact of out
of school play and getting along with others on overall academic performance. In this
regression, student gender, attendance in class, out of school play, and getting along with
others are the predictors (independent variables) and overall academic performance is the
dependent variable.
This hierarchical regression seeks to answer the following:
• How does each model explain the impact of its independent variable(s) on overall
academic performance?
• How much change in academic performance (dependent variable) can I predict based
on the model’s independent variable(s)?
R-square (0.002) in Model 1 means that 2% of the variance in overall academic performance is
explained or accounted for by gender. Model 1 is not significant at .674 level, with an F change
of .178, and degrees of freedom 1,114.
R-square (0.346) in Model 2 means that 34.6% of the variance in overall academic
performance is explained by Gender and Attendance. The R-square change is .345, which
means that 34.5% of the variance is added to Model 1 by including the variable of attendance.
The model is significant at .000 level, with an F change of 59.557, and degrees of freedom
1,113
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6. Intermediate Statistics Final Exam
Michael Parent
R-square (.634) in Model 3 means that 63.4% of the variance in overall academic performance
is accounted for by Gender, Attendance and "Out of school I play (hang out with friends)". The
R-square change is .288, which means that 28.8% of the variance in overall academic
performance is added to Model 2 by including the variable "Out of school I play (hang out with
friends)". It is significant at the .000 level, with an F change of 43.650, and degrees of freedom
2,11
When reviewing the ANOVA table:
• The first regression model, is not significant at .674 level, with an F value of .178,
degrees of freedom 1,114. This means that student gender is not a significant predictor
of overall academic performance.
• The second regression model, is significant at the .000 level, with an F value of .
29.913, degrees of freedom 2,113. This means that student gender and attendance
combined is a significant predictor of overall academic performance.
• The third regression model, is significant at .000 level, with and F value of 48.072,
degrees of freedom 4,111. This means that student gender, attendance and out of
school I play (hang out with friends) combined is a significant predictor of overall
academic performance.
A careful examination of the standardized coefficient (or beta) reveals the following:
Model 1 Summary
• Gender has a beta of .039 and is not a significant predictor at .674 level, with a t value of .
422. This model indicates that Gender is not a significant predictor of overall academic
performance.
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7. Intermediate Statistics Final Exam
Michael Parent
Model 2 Summary
• Gender has a beta of .127 and is not a significant predictor at the .103 level, with a t value of
1.646.
• Attendance has a beta of .593 and is significant at the .000 level, with a t value of 7.717.
This model indicates that attendance is a significant predictor of overall academic achievement.
Although gender's beta increased from .039 in Model 1 to a beta of .127 in Model 2, it is still not
a significant predictor.
Model 3 Summary
• Gender with a beta of .097 is not a significant predictor at the .098 level, with a t
value of 1.668.
• Attendance is a significant predictor at the .000 level, with a beta of .327, with a t
value of 3.892.
• "Out of school I play (hang out with friends)" is not a significant predictor at the .662
level, with a beta of -.026 and a t value of -.439.
• "Getting along w/ other students" is significant at .000 level, with a t value of 9.109,
with a beta of .542.
In Model 3, attendance lost significance as a predictor (it had a beta of .593 in Model 2, but a
beta of .274 in Model 3). After examining the three models, "Getting along with other students"
is the most powerful predictor of overall academic performance.
Model 3 is the best model for predicting overall academic achievement when combining the
predictors of "Attendance in class" and the predictor of "Getting along with other students".
It explains the most variance in overall academic achievement. "Getting along with Students"
(beta=.542) is the most powerful predictor in the model. "Attendance" (beta=.236) is the second
most powerful predictor of overall academic achievement.
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8. Intermediate Statistics Final Exam
Michael Parent
Recommendations
This study examined the 140 fourth and fifth grade students’ behaviors (both in and out of
school) as a means of developing an “arts intervention” program that would be infused in the
teaching of language arts and social studies. This requires one to carefully consider when to
implement an arts intervention program.
The SPSS profile plots outputs reveal that 4th grade males and 5th grade females report
strikingly different out of school play patterns; 4th grade males tend to hang out with friends more
than do 4th grade females – but by the 5th grade, females report a higher rate of hanging out with
friends than do 5th grade males. When controlling for “out of school I play organized sports” in
the student out of school activities reporting, the female students report a higher degree of out
of school play than do the males. In fact, nearly half of the male students (between the 4th and
5th grades) do not hangout with friends after school. Based on the profile plots data, it is strongly
recommended that an arts intervention program be implemented into the 4th grade.
After reviewing the data provided, "getting along with others" is the dominant predictor of overall
academic performance. Thus, an important part of an arts intervention program must include an
element that allows students to form and engage in positive and supportive peer relationships.
This can be accomplished through group arts activities, positive role-play, character education
programming, and designing class projects that encourage peer cooperation while muting
competition. The arts, by their very nature, lend themselves to promoting “getting along with
others”.
“Attendance” is the next strongest predictor of overall academic performance. When designing
an art intervention program – or any intervention program – the school will have to address
student “buy in”. Students will need a reason to come to school or class. Perhaps the arts
intervention program would include an attendance incentive measure; students are credited in
some way for a positive attendance record. Likewise, the program itself must be designed in
such a way as to interest the students – field trips to museums, the theater, operas, or other
arts-related venues might spurn student interest in the arts and, subsequently, school.
It is vital that the arts intervention program be infused into the school day and that after school
programming be avoided; the data shows that half of the male students do not hangout with
friends after school, thus many of these students would not voluntarily participate in an arts
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9. Intermediate Statistics Final Exam
Michael Parent
intervention program if it were held after school hours. Although the same is not true for female
students, an integrated arts intervention program during school hours would yield a higher rate
of attendance and participation.
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