HSAG Report - Alison Chapman and Allison Makowski_PDF

EVALUATING GEOLOGY TOPICS IN
STANDARDIZED TESTING
A STATISTICAL CONSULTING EXPERIENCE
GRAND VALLEY STATE UNIVERSITY
STA 319-02: STATISTICS PROJECT
4/21/15
ALISON CHAPMAN AND ALLISON MAKOWSKI

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Table of Contents:

Abstract 2
Introduction 3
Methods 5
Results 7
Hypothesis 1 12
Hypothesis 2 13
Hypothesis 3 14
Hypothesis 4 15
Hypothesis 5 16
Discussion/Recommendations 17
Appendix 19

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Abstract:

The purpose of this project was to evaluate geology topics in standardized testing. This
report analyzes the High School Advanced Geology (HSAG) exam scores. A GVSU Geology
professor named Dr. Steve Mattox created the HSAG exam. The HSAG exam covers 12-15
geology topics is composed of four parts: Multiple Choice, Rocks and Minerals, Maps, and an
Essay portion. The data was collected from high school seniors in nine different schools between
2012-2014. Analyses were conducted to recognize the areas where the students struggled. After
the analyses were completed, we found that the student’s total score on the HSAG exam differed
between the nine schools. Also, there was a difference in the student’s score between the four
portions of the HSAG exam for five of the nine schools: Dream Academy, Grosse Point South,
Grand Haven, Hudsonville, Multicultural Academy. Our findings will allow Dr. Mattox to look
at specific parts of the exam where student’s struggled and modify the exam to aid in more
students passing. The results will also let Dr. Mattox inform the teachers where his/her students
struggled, so he/she can adjust their lectures so more students in the school can pass.

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Introduction:

The High School Advanced Geology (HSAG) exam was designed high school seniors
that that were currently taking a geology course. The HSAG exam acts like an Advanced
Placement (AP) exam, where students can pass and earn college credit. Our client, Dr. Steve
Mattox, developed the HSAG exam. Dr. Mattox is a GVSU Geology professor and he was
assisted in this project by a GVSU Earth Science student named Christina Sobolak. This project
was funded by two National Science Foundation (NSF) grants, which allowed Dr. Mattox to
expand the project by adding more schools and getting teachers supplies to use in their classroom
lectures. The schools that were ideal for this project were those high in diversity and had a
teacher with an Earth Science minor, Geology major, or Masters in Science education. This
project offers summer training for the teachers along with materials to supply the classroom.
Our role in this study was to act as lead statistical consultants. Dr. Mattox and Christina
collected all of the necessary data, while we ran the statistical analyses. Dr. Mattox wanted to
identify specific topics that caused the most difficulty for students. These topics could prevent
students from passing the exam. The ultimate goal of this program is to help increase the number
of high school students taking a geology course and the level of geology knowledge of
participating teachers and students. Dr. Mattox would like to make this HSAG course to be as
qualified as current AP science courses. Our findings will be able to aid Dr. Mattox in the
continuation of this project. Dr. Mattox would be able to provide the teachers with additional
training and other resources to help future students learn better. The findings will also aid in
increasing the number of students passing the HSAG exam/earning credit, as well as increasing
the number of students enrolling in advanced college geoscience courses. Having more students

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enroll in geoscience courses will hopefully aid in more students pursing a geoscience career,
which is a field of study where there is a projected shortage of graduates.
In order to assist Dr. Mattox with his project, we conducted statistical analyses to find
significant results. We did this by answering specific hypotheses that we created.
The five hypotheses that we tested are as follows:
1. Is there is a difference in the students’ mean section percent between the four portions
of the HSAG exam?
2. Is there is a difference in the students’ total mean percent on the HSAG exam
between the years?
3. Is there is a difference in the students’ total mean percent on the HSAG exam
between the nine schools?
4. Is there is a difference in the FOCUS students’ mean section percent between the 4
portions of the HSAG exam?
5. Looking at each individual school, is there a difference in the students’ mean section
percent between the four portions of the HSAG exam

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Methods:

The HSAG exam consisted of four separate portions: Multiple Choice, Rocks and
Minerals, Maps, and an Essay portion. The HSAG exam is often taken in the spring, but each of
the four portions may be taken at separate times. The HSAG exam consists of approximately 12
to 15 general geology topics. There were a total of 196 questions, worth 377 points, on the
HSAG exam. The Multiple Choice portion had the most questions out of all the portions, and the
Essay portion was the shortest portion. Table 1 below, shows the number of questions on each
portion and the amount of geology topics covered within the portion.
Table 1: Questions, Topics, and Points for Each Portion of the HSAG Exam
Portion of the
HSAG Exam
Number of
Questions
Number of
Geology Topics
Total Number of
Points
Multiple Choice 77 13 152
Rocks and Minerals 50 4 100
Maps 40 10 80
Essay 29 6 45
Point distribution between the four portions can be seen below in Figure 1. There are
currently nine Michigan colleges and universities that have awarded students with college if the
student gets a 70% or better on the exam. If the student gets a passing score (70% or better), they
will receive up to four college credits. The data collected by Dr. Mattox and Christina ranges
from 2012 to 2014, with approximately four to eight schools participating each year. This data
includes every student who took the exam along with their total number of points they received
for each portion of the exam.

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Figure 1. Point Distribution of Each Portion of the HSAG Exam
The data was collected from nine different schools in Michigan between 2012 and 2014.
Table 2 shows which schools were involved and the year they participated. There were only
three schools that participated in all three years (Grosse Point South, Hudsonville, and Okemos).
Table 2. The Years the Schools Were Sampled
Year
Black
River
Cody
DIT
Dream
Academy
Grand
Haven
Grosse
Point
South
Henry
Ford
Hudsonville
Multicultural
Academy
Okemos
2012 X X X X
2013 X X X X X X
2014 X X X X X X X X
Dr. Mattox recorded the collected data and entered it into Excel files that were separated
by school and by year. The students’ total score on the exam, as well as their score for each
portion were recorded within the Excel files. In our study, we analyzed the sample of 354 high
school students.

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Results:

We were given the data in 18 excel files, so we had to restructure the data. Because of
how our data was originally formatted, we needed to combine the multiple Excel files into a
single Excel file that could easily be inputted into a software package. We did this by “copying
and pasting” the data that was needed from each Excel spreadsheet into a single Excel
spreadsheet. Upon doing this, we discovered a few missing values. We replaced the missing
values with zeros because a lack of a value indicated that the student did not take a portion of the
exam, or the complete HSAG exam. Not taking the exam resulted in that student receiving a 0%
on the portion or the exam. No other data cleaning technique was needed. Any errors in the data
would have been from a mistake in the inputting of the original data values by Dr. Mattox. We
would not be able to discover these errors. After restructuring and cleaning the data, we used
SPSS 20 and SAS 9.3 to conduct our analyses.
We began by creating new variables in SPSS and SAS. First, we had SPSS calculate the
percent that a student earned on each of the four portions of the exam. SPSS also calculated the
percent that a student earned on the HSAG exam in total. The following variables were created
by SPSS: Multiple Choice Percentage, Maps Percentage, Rocks and Minerals Percentage, Essay
Percentage, and Total Exam Percentage.
Dr. Mattox also wanted to examine the students that scored between 40-69.99% on the
HSAG exam to see where they struggled. We called these students the Focus students. In order
to accomplish this, we had SAS create a new variable for the focus students by selecting the
students that scored between a 40% and 69.99% on the HSAG Exam. We did not need any
further data reconstructing. As a whole, our dataset did not require much SPSS or SAS
manipulation, besides the creation of new variables.

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Our project consisted of seven key variables of interest: Portion Percent, School, Year,
Portion of the HSAG Exam, Total Exam Percent, Students, and Focus Students. Information,
about the key variables such as the type, values, and description, is shown in Table 3.
Table 3. Information on the Key Variables in Our Study
Variable Name
Variable
Type
Range/Values the
Variable Can Take On
Variable Description
Portion
Percent
Quantitative 0 % - 100 %
The percentage that a student
received for a portion of the
HSAG Exam
School Categorical
Black River
Cody DIT
Dream Academy
Grand Haven
Grosse Point
South
Henry Ford
Hudsonville
Multicultural
Academy
Okemos
The school where the student
took the HSAG Exam
Year Categorical 2012 2013 2014
The year that a student took the
HSAG Exam
Portion of the
HSAG Exam
Categorical
Multiple Choice
Rocks and
Minerals
Maps
Essay
The portion of the HSAG Exam
Total Exam
Percent
Quantitative 0 % - 100 %
The percentage that a student
received on the HSAG Exam
Students Categorical Each student had a specific ID
Any student that took the
HSAG Exam
Focus Students Categorical
0 or 1 (NO or YES)
“0” = “NO”—Not a focus student
“1” = “YES”—Is a focus student
Any student that took the HSAG
Exam and scored between a
40 % - 69.99 %

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For the quantitative key variables, the maximum, minimum, and mean values were
calculated in SPSS. The values can be found in Table 4. Between all nine schools and all three
years, the highest average percent was for the Essay portion at 60.39%. The lowest average
percent belonged to the Maps portion at 55.17%. As a whole, the average percent on the HSAG
Exam was 58.17%.
Table 4. Descriptive Statistics of the Quantitative Variables
(Portion Percent and Total Exam Percent)
Variable Name Mean Minimum Maximum
Portion
Percent
Multiple Choice
Percent
59.02 % 0 % 99 %
Rocks and Minerals
Percent
58.27 % 0 % 100 %
Maps
Percent
55.17 % 0 % 98 %
Essay
Percent
60.39 % 0 % 98 %
Total Exam
Percent
HSAG Exam
Percent
58.17 % 0 % 95 %
For the categorical variables, the frequencies were calculated. The frequencies for the
variable Year is shown in Figure 2. As shown in Figure 2, the number of students sampled per
year increased between 2012-2014. This is because each year had more schools participating
than the previous. The sampling of the schools is shown in Table 2.

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Figure 2. Frequencies of the Variable Year
The frequencies for the variable School are shown in Figure 3. As shown in Figure 3, the
school with the most students sampled is Hudsonville with 138 students. On the other hand,
Multicultural Academy and Henry Ford had the lowest amounts, with 4 and 5 students,
respectively.
Figure 3. Frequencies of the Variable School
86
120
148
0
20
40
60
80
100
120
140
160
2012 2013 2014
Number of Students Sampled Per Year (all schools)
138
49
47
40
35
19
17
5
4
0 20 40 60 80 100 120 140 160
Hudsonville
Grosse Point South
Okemos
Grand Haven
Black River
Dream Academy
Cody DIT
Henry Ford
Multicultural Academy
Number of Students Sampled for Each School (all years)

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For our variable, Focus Student, there were a total of 101 out of the 354 students that
scored between a 40% - 69.99%. If the student was a Focus Student, they had a value equal to
“Yes”. Otherwise, the student’s value was equal to “No”. Figure 5 shows the frequencies of the
Focus Students variable.
Figure 4. Frequencies of Variable Focus Students
For each of our hypotheses (except for hypothesis three), a statistical test called an
Analysis of Variance (ANOVA) was used. An ANOVA test is a statistical test of whether or not
the means of several groups are equal or not. We can conclude that there is significant evidence
of a difference in the means if our p-value is less than 0.05. There are three assumptions for an
ANOVA test to be valid: (1) we have independent observations, (2) the samples come from a
normal distribution, and (3) the variances of the data in the groups are equal.
If the assumptions are not met, like in hypothesis three, a nonparametric equivalent to an
ANOVA test, called a Kruskal-Wallis test, is used. A Kruskal-Wallis test ranks the data to help
determine if there is significant evidence of a difference in at least one of the distributions. It is a
significant result if our p-value is less than 0.05. However, the Kruskal-Wallis test is not as
powerful as an ANOVA, but it is useful when the assumptions are not met for an ANOVA test.

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Hypothesis 1: Is there a difference in the students’ mean section percent between the four
portions of the HSAG exam?
First, we tested to see what portion of the exam caused the students the most difficulty.
We ran a One-Way ANOVA test to address this hypothesis. The average students’ scores on
each portion of the exam is shown in Table 5. Because our p-value was 0.084, we were not able
to conclude that there was a difference in the students’ mean scores between the four portions of
the HSAG exam. The Map portion of the HSAG exam had the lowest mean percent, but we
cannot conclude that it was significantly different than the other portions of the exam. The
complete test that was conducted in SPSS for Hypothesis 1 can be seen in the Appendix A.
Table 5. Descriptive Statistics of Student’s Mean Percentage for Each Portion of the Exam
Name Mean
Standard
Deviation
Multiple Choice
Percent
59.02 % 27.38 %
Rocks and
Minerals Percent
58.27 % 27.95 %
Maps Percent 55.17 % 26.65 %
Essay Percent 60.39 % 29.96 %

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Hypothesis 2: Is there a difference in the students’ total mean percent on the HSAG exam
between the years?
Next, we tested to see if the students’ total mean percent changed over the course of the
three years. For this hypothesis, we also ran a One-Way ANOVA. The average students’ scores
for each year is shown in Table 6. The lowest mean score on the HSAG exam was in 2014 with a
score of 55.47%. The highest mean score on the HSAG exam for all the students was in 2012
with a score of 63.87%. However, our p-value was 0.056 so there was not significant evidence to
indicate that the students’ mean score differs between the years. We found these results to be
surprising because the average scores actually went down as time went on. Before running the
test, we assumed the scores would increase because teachers could change their teaching styles
to better prepare future students. However, over the course of the three years, the program
expanded the number of schools participating each year. The results could have been “diluted”
by adding schools that were not as prepared to take the HSAG exam unlike the other schools that
have been in the program before. There were several schools that only took this exam in one of
the years so these teachers were not given the opportunity to change and enhance their teaching
strategies yet. The complete test for Hypothesis 2 can be seen in the Appendix B.
Table 6. Descriptive Statistics of the Student’s Total Percentage in Each Year
Year Mean
Number of
Students
2012 63.87 % 86
2013 57.41 % 120
2014 55.47 % 148

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Hypothesis 3: Is there a difference in the students’ total mean percent on the HSAG exam
between the nine schools?
Our next test was to determine if the students’ total mean percent differed between the
nine schools. Our first choice was to run a One-Way ANOVA, to address this hypothesis, but our
assumptions were not met. Therefore, we decided to run the nonparametric equvialnt to an
ANOVA called a Kruskal-Wallis test. With a p-value less than 0.001, we found significant
evidence of a difference in the students’ total mean percent on the HSAG exam between the nine
schools. The total sample size for each school, as well as the students’ mean rank on the HSAG
exam can be seen in Table 7. You can see that Hudsonville had the highest mean rank of 269.88.
However, Hudsonville has taken this exam for over 10 years, so the teacher has perfected his
teaching style. We can than compare this to Cody DIT who had the lowest mean rank of 49.76
and took the exam only in 2013 and 2014. The complete test for hypothesis 3 can be seen in the
Appendix C.
Table 7. Descriptive Statistics of Each School’s Total Exam Percentage Ranked
School
Number of
Students
Average Rank
Black River 35 122.77
Cody DIT 17 49.76
Dream Academy 19 26.58
Gross Point South 49 180.98
Grand Haven 40 163.36
Henry Ford 5 67
Hudsonville 138 269.88
Multicultural Academy 4 78.38
Okemos 47 82.81

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Hypothesis 4: Is there a difference in the Focus students’ mean section percent between the
four portions of the HSAG exam?
We also wanted to test to see what portion of the HSAG exam caused the Focus students
the most difficulty. We ran a One-Way ANOVA test to address this hypothesis. The average
Focus Students’ scores for each portion of the HSAG exam and the exam in total are shown in
Table 8. With a p-value less than 0.001, we found significant evidence to show that the Focus
Students’ mean score differs between the four portions of the exam. The Essay’s mean
percentage was significantly greater than the other three portions of the exam at 60.89%, on
average. The lowest mean score for the Focus Students group was the Multiple Choice portion
with an average score of 53.30%. The complete analysis for Hypothesis 4 can be found in the
Appendix D.
Table 8. Descriptive Statistics of Focus Student’s Mean Percentage
(Each Portion Percent and Total Percent Overall)
Portion Mean
Multiple Choice
Percent
53.30 %
Rocks and
Minerals Percent
54.87 %
Maps
Percent
55.54 %
Essay
Percent
60.89 %
HSAG Exam
Percent TOTAL
56.14 %

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Hypothesis 5: Looking at each individual school, was there a difference in the students’
mean section percent between the four portions of the HSAG exam?
Lastly, we wanted to look at each individual school to see what portion of the HSAG
exam caused their students the most difficulty. We ran a One-Way ANOVA test to address our
hypothesis. We found insufficient evidence that there was a difference in students’ mean
percentage between the 4 portions of the HSAG exam for the following schools: Black River,
Cody DIT, Henry Ford, and Okemos. However, we did find significant evidence that there was a
difference in students’ mean percentage between the 4 portions of the HSAG exam for Dream
Academy, Grosse Point South, Grand Haven, Hudsonville, and Multicultural Academy. In Table
9, the portion of the exam that caused those five schools the most difficulty is shown. The
complete test conducted in SPSS for hypothesis 5 can be seen in Appendix E.
Table 9. Schools’ Lowest Mean Portion of Exam for the Significant Results
School
Multiple
Choice
Rocks and
Minerals
Maps Essay
Dream Academy X X
Grosse Point South X X X
Grand Haven X
Hudsonville X
Multicultural Academy X X

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Discussion/Recommendations:

Our data analysis allowed Dr. Mattox to look at specific portions of the exam instead of
the entire HSAG exam. Dr. Mattox wanted to focus most of his attention on the students that
scored between a 40% - 69.99%, since they are the students that were close to passing, but
missed the mark. After running our analyses, we would recommend that Dr. Mattox re-look at
the multiple choice portion of the exam, since there was significant evidence that this portion
caused those students that scored between a 40% - 69.99% the most difficulty. This will help Dr.
Mattox to spend his time, energy, and resources on that specific portion, instead of spreading it
across the whole exam.
We also were able to show Dr. Mattox how each individual school was performing,
which will allow him to adjust the schools that he has in the program. By showing how each
school is performing, Dr. Mattox will be able to decide if he will drop a school from his program
and invest his resources in a school that is better suited for the program. This will help the
schools that are dedicated to the program by helping those schools continue to do better.
Our analyses will also allow Dr. Mattox to contact the teachers within the program to
show them where their particular students struggled. This will help the teachers in the program
adjust their teaching to better prepare future students. The teachers will be able to adapt based on
this data and change their strategies to fit the students’ needs.
Dream Academy should focus on improving the topics in the rocks and minerals portion
as well as the essay portion. Grosse Point South should focus on improving all the topics in all
the portions besides the essay portion. On the other hand, Grand Haven and Hudsonville only
need to focus on the topics in the multiple choice and map portion; respectively. Lastly,
Multicultural Academy should concentration on the topics in the Map and Essay portions.

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There are a few limitations with the data since the same schools were not consistently
sampled for each of the years, but this is due to the program being expanded and allowing more
schools to participate. A few suggestions for further research would be to continue to add more
schools to the program and let the current teacher’s know where he or she can better focus his or
her teaching.

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Appendix:
Appendix A: Hypothesis 1 20
Appendix B: Hypothesis 2 23
Appendix C: Hypothesis 3 27
Appendix D: Hypothesis 4 30
Appendix E: Hypothesis 5 33
School 1: Black River 33
School 2: Cody DIT 35
School 3: Dream Academy 37
School 4: Grosse Point 39
School 5: Grand Haven 41
School 6: Henry Ford 43
School 7: Hudsonville 45
School 8: Multicultural Academy 47
School 9: Okemos 49

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Appendix A: Hypothesis 1
Goal/Hypothesis:
To determine if there is a difference in the students’ mean portion score
between the four portions of the HSAG exam
Figure A.1 shows the variability of the student’s mean score for each portion. Each boxplot
shows the same amount of variability and all four are very similar.
Figure A.1. Boxplots of Each Portion of the HSAG Exam
Figure A.2. SPSS Output for the Average Percent for Each Portion of the HSAG Exam

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We are analyzing a quantitative dependent variable (Portion Percent) by a qualitative
independent variable with four categories (Portion of the HSAG Exam), so we will be using a
One-Way ANOVA test for this hypothesis.
Assumptions for a One-Way ANOVA:
1. Independent samples
This assumption is met because each student’s score on one portion of the
HSAG Exam is independent of the other portions.
2. Approximately Normal Populations
From Figure A.3, each portion has a skewness and kurtosis value between
(-1,1) so we can accept normality, which means the students’ mean score on each
portion of the HSAG exam is from a normal population. This assumption is met.
Figure A.3. Skewness and Kurtosis SPSS Output
3. Equal Variances
In order to check for equal variances, we will be using a statistical test
called the Levene’s Test, which will tell us if the variances for each of the
portions of the exam are approximately equal.
From Figure A.4, we see the test produces a test statistic of 2.019 and a
p-value of 0.109, so we can conclude that there is significant evidence of equal
variances across the four portions of the HSAG Exam.
This assumption is met.
Figure A.4. Levene’s Test SPSS Output

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Since all three of the assumptions are met, we will proceed with the One-Way ANOVA.
Figure A.5. SPSS Output for the One-Way ANOVA Test for Hypothesis 1
From Figure A.5, we see that our One-Way ANOVA test results in a test statistic of
F = 2.219, which produces a p-value = 0.084. Our p-value is large, so we do not have a
significant result. This means that there is not significant evidence that there is a difference in
students’ mean scores between the 4 portions of the HSAG exam.

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Appendix B: Hypothesis 2
Goal/Hypothesis:
To determine if there is a difference in the students’ total mean percent on the
HSAG exam between the years
Figure B.1 shows the variability of the student’s total mean score for each year. The boxplots
show approximately the same shape, but we will check the assumptions.
Figure B.1. Boxplots of Each Year
Figure B.2. SPSS Output for the Average Total Percent for Each Year

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We are analyzing a quantitative dependent variable (Total Percent) by a qualitative
independent variable with three categories (Year), so we will be using a One-Way ANOVA test
for this hypothesis.
This assumption is met because each student’s total score on the HSAG
Exam from one year is independent of the other years.
From Figure B.3, the year 2012 has a skewness and kurtosis value
between (-1,1) so we can accept normality for this year, which means the
students’ mean score on the HSAG exam in 2012 is from a normal population.

Figure B.3. Skewness and Kurtosis SPSS Output for 2012

From Figure B.4, the year 2013 has a skewness value between (-1,1), but
the kurtosis value is outside the “normal” range. At a -1.005, the kurtosis value is
not extremely far off what we would consider “normal”, so we will proceed on
assuming normality for this year. This means the students’ mean score on the
HSAG exam in 2013 is from an approximately normal population.


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From Figure B.5, the year 2014 has a skewness value between (-1,1), but
the kurtosis value is outside the “normal” range. At a -1.240, the kurtosis value is
close to what we would consider “normal”, so we will proceed with caution on
accepting normality for this year. This means the students’ mean score on the
HSAG exam in 2014 is from an approximately normal population.

Combining all of the information from figure B.3, B.4, and B.5, we will
continue with assuming normality since the skewness and kurtosis values for all
three years are not extreme and we also have a large sample size. This assumption
is met.
3. Equal Variances
From Figure B.5, we see the test produces a test statistic of 0.740 and a
p-value of 0.478, so we can conclude that there is significant evidence of equal
variances across the three years.
This assumption is met.
Figure B.5. Levene’s Test SPSS Output

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From Figure B.6, we see that our One-Way ANOVA test results in a test statistic of
F = 2.904, which produces a p-value of 0.056. Our p-value is above our significance level of
0.05, so we do not have a significant result. This means that there is not significant evidence to
show that the students’ mean score differs between the years.
Figure B.6. SPSS Output for the One-Way ANOVA Test for Hypothesis 2

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Appendix C: Hypothesis 3
Goal/Hypothesis:
To determine if there is a difference in the students’ total mean percent on the
HSAG exam between the nine schools
Figure C.1 shows the variability of the student’s total mean score for each school and there is an
enormous difference in variability between the nine schools.
Figure C.1. Boxplots of Each School
We are analyzing a quantitative dependent variable (Total Percent) by a qualitative
independent variable with nine categories (School), so we will be using a One-Way ANOVA test
for this hypothesis if the assumptions are met.

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This assumption is met because each student’s total score on the HSAG
Exam from one school is independent of the other schools.
This assumption is met for the most part because we have a large sample
size for most of the school, but there are a few schools that have a smaller sample
size. We will continue checking the assumptions with reservations.
Figure C.3. Descriptive Statistics
3. Equal Variances
From Figure B.4, we see the test produces a test statistic of 13.298 and a
very small p-value of less than 0.000, so we CANNOT conclude that there are
equal variances across the nine schools. This assumption is NOT met.
Figure C.3. Levene’s Test SPSS Output

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Since all the assumptions are NOT met, we cannot proceed with the One-Way ANOVA.
We will be conducting a Kruskal-Wallis Test instead.
From Figure C.4, we see that our Kruskal-Wallis test results in a test statistic of
χ2
(8) = 240.944 which gave us a p-value less than 0.000. Therefore, we have significant evidence
of difference in the students’ total percent between the nine different schools,
Figure C.4. SPSS Output for the Kruskal-Wallis Test for Hypothesis 3
There is a mean rank score of 26.58 for Dream Academy, 49,76 for Cody DIT, 67 for
Henry Ford, 78.38 for Multicultural Academy, 82.81 for Okemos, 122.77 for Black River,
163.36 for Grand Haven, 180.98 for Grosse Point South, and 269.88 for Hudsonville. The results
are shown in Figure C.5.

Figure C.5. SPSS Output for Ranks for Each School

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Appendix D: Hypothesis 4
Goal/Hypothesis:
To determine if there is a difference in the Focus Students’ mean section
percent between the 4 portions of the HSAG exam
Figure D.1. Shows the variability of the Focus Students’ mean score for each portion of the
HSAG Exam.
Figure D.1. Boxplots of Each Portion of the HSAG Exam for the Focus Students
Figure D.2. SPSS Output for the Focus Students’ Average Percent for Each Portion of the
HSAG Exam

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We are analyzing a quantitative dependent variable (Focus Students’ Portion Percent) by
a qualitative independent variable with four categories (Portion of the HSAG Exam), so we will
be using a One-Way ANOVA test for this hypothesis.
This assumption is met because each focus student’s score on one portion
of the HSAG Exam is independent of the other portions.
From Figure D.3, we have p-values for the Shapiro-Wilk Test for
Normality that are all significant (greater than 0.05). Therefore, we can assume
normality. Thus, this assumption is met.
Figure D.3. Shapiro Wilk Test for Normality Results
3. Equal Variances
From Figure D.4, we see the test produces a test statistic 2.173 and a p-
value of 0.091, so we can conclude that there is significant evidence of equal
variances across the four portions of the HSAG Exam. This assumption is met.
Figure D.4. Levene’s Test SPSS Output

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From Figure D.5, we see that our One-Way ANOVA test results in a test statistic of
F = 6.175, which produces a p-value less than 0.000. Our p-value is very small, so we have a
significant result. This means that there is significant evidence to that the focus students’ mean
score differs between the four portions of the exam.
Figure D.5. SPSS Output for the One-Way ANOVA Test for Hypothesis 4

Figure D.6 shows the portions of the exams are significantly different from each other.
The essay portion has a higher mean score than the multiple choice, rocks and minerals, and
maps portions. We can conclude that the focus students’ scored significantly higher on the essay
portion of the HSAG exam.
Figure D.6. SPSS Output Focus Students

33
Appendix E: Hypothesis 5
Goal/Hypothesis: Is there a difference in the students’ mean section percent between the
four portions of the HSAG exam
School 1: Black River
Figure E.1 shows the variability of Black River’s students’ mean score for each portion.
Each boxplot has a different shape, and they do not look similar. We suspect that our ANOVA
assumptions will not be met.
Figure E.1. Boxplots of Each Portion of the HSAG Exam
We will only check for equal variances since we presume this assumption will not be
met. From Figure E.2, we see the test produces a test statistic 3.875 and a p-value of 0.011, so we
cannot conclude that there is significant evidence of equal variances across the four portions of
the HSAG Exam for the students of Black River.
Figure E.2. Levene’s Test SPSS Output for Black River

34
Since this assumption was NOT met, we cannot proceed with the One-Way ANOVA. We
will be conducting a Kruskal-Wallis Test instead.
From Figure E.3, we see that our Kruskal-Wallis test results in a test statistic of
χ2
(3) = 1.776 which gave us a p-value of 0.620. Therefore, there is not significant evidence to
show that there is a difference in Black River’s students’ mean section score between the four
portions of the HSAG exam.
Figure E.3. Kruskal-Wallis Test for Black River

35
School 2: Cody DIT
Figure E.4 shows the variability of Cody DIT students’ mean score for each portion.
Figure E.4. Boxplots of Each Portion of the HSAG Exam for Cody DIT
We will only check for equal variances since we have a large sample to assume normality
and independent samples. From Figure E.5, we see the Levene’s test produces a test statistic of
2.054 and a p-value of 0.115, so we conclude that there is significant evidence of equal variances
across the four portions of the HSAG Exam for the students of Cody DIT.
Figure E.5. Levene’s Test SPSS Output for Cody DIT

36
From Figure E.6, we see that our One-Way ANOVA test results in a test statistic of
F = 1.019, which produces a p-value of 0.390. This means that there not significant evidence that
there is a difference in Cody DIT’s students’ mean section score between the four portions of the
HSAG exam.
Figure E.6. SPSS Output for the One-Way ANOVA Test for Cody DIT

37
School 3: Dream Academy
Figure E.7 shows the variability of Dream Academy’s students’ mean score for each portion.
Figure E.7. Boxplots of Each Portion of the HSAG Exam for Dream Academy
and independent samples. From Figure E.8, we see that the Levene’s test produces a test statistic
of 1.680 and a p-value of 0.179, so we conclude that there is significant evidence of equal
variances across the four portions of the HSAG Exam for the students of Dream Academy.
Figure E.8. Levene’s Test SPSS Output for Dream Academy

38
From Figure E.9 we see that our One-Way ANOVA test results in a test statistic of
F = 6.326, which produces a p-value of 0.001. This means that there is significant evidence that
there is a difference in Dream Academy’s students’ mean section score between the four portions
of the HSAG exam.
Figure E.9. SPSS Output for the One-Way ANOVA Test for Dream Academy

In order to see which portion causes the school the most difficulty, we ran a Tukey HSD
post-hoc procedure so we can analyze which portion results in a significant difference from the
other portions. Figure E.10 shows that the lowest mean value is essay and rocks and minerals for
the Dream Academy students.
Figure E.10. Tukey HSD Test for Dream Academy

39
School 4: Grosse Point South
Figure E.11 shows the variability of Grosse Point South’s students’ mean score for each portion.
Figure E.11. Boxplots of Each Portion of the HSAG Exam for Grosse Point South
and independent samples. From Figure E.12, we see that the Levene’s test produces a test
statistic of 1.040 and a p-value of 0.376, so we conclude that there is significant evidence of
equal variances across the four portions of the HSAG Exam for the students of Grosse Point
South.
Figure E.12. Levene’s Test SPSS Output for Grosse Point South

40
there is a difference in Grosse Point South’s students’ mean section score between the four
Figure E.13. SPSS Output for the One-Way ANOVA Test for Grosse Point South

other portions. Figure E.14 shows that the lowest mean value are rocks and minerals, maps, and
multiple choice for the Grosse Point South’s students.
Figure E.14. Tukey HSD Test for Grosse Point South

41
School 5: Grand Haven
Figure E.15 shows the variability of Grand Haven’s students’ mean score for each
portion. Each boxplot has a different shape, and they do not look similar. We suspect that our
ANOVA assumptions will not be met.
Figure E.15. Boxplots of Each Portion of the HSAG Exam for Grand Haven
met. From Figure E.16, we see the Levene’s test produces a test statistic 3.048 and a p-value of
0.030, so we cannot conclude that there is significant evidence of equal variances across the four
portions of the HSAG Exam for the students of Grand Haven.
Figure E.16. Levene’s Test SPSS Output for Grand Haven

42
χ2
(3) = 10.188 which gave us a p-value of 0.017. Therefore, there is significant evidence to show
that there is a difference in Grand Haven’s students’ mean section score between the four
Figure E.17. Kruskal-Wallis Test for Grand Haven

In order to see which portion causes the school the most difficulty, we ran a post-hoc
procedure so we can analyze which portion results in a significant difference from the other
portions. Figure E.18 shows that the lowest mean value is multiple choice for the Grand Haven’s
students.
Figure E.18. Post Hoc for Grand Haven

43
School 6: Henry Ford
Figure E.19 shows the variability of Henry Ford’s students’ mean score for each portion.
Figure E.19. Boxplots of Each Portion of the HSAG Exam for Henry Ford
We will only check for equal variances since we assume high variability in the boxplots.
From Figure E.20, we see that the Levene’s test produces a test statistic of 2.971 and a p-value of
0.063, so we can conclude that there is significant evidence of equal variances across the four
portions of the HSAG Exam for the students of Henry Ford.
Figure E.20. Levene’s Test SPSS Output for Henry Ford

44
F = 0.148, which produces a p-value of 0.929. This means that there is not significant evidence
that there is a difference in Henry Ford’s students’ mean section score between the four portions
of the HSAG exam.
Figure E.21. SPSS Output for the One-Way ANOVA Test for Henry Ford

45
School 7: Hudsonville
Figure E.22 shows the variability of Hudsonville’s students’ mean score for each portion.
Each boxplot has a different shape, and they do not look similar. We suspect that our ANOVA
assumptions will not be met.
Figure E.22. Boxplots of Each Portion of the HSAG Exam for Hudsonville
met. From Figure E.23, we see the Levene’s test produces a test statistic 3.220 and a p-value of
0.022, so we cannot conclude that there is significant evidence of equal variances across the four
portions of the HSAG Exam for the students of Hudsonville.
Figure E.23. Levene’s Test SPSS Output for Hudsonville

46
χ2
(3) = 62.992 which gave us a p-value less than 0.000. Therefore, there is significant evidence
to show that there is a difference in Hudsonville’s students’ mean section score between the four
Figure E.24. Kruskal-Wallis Test for Hudsonville

In order to see which portion causes the school the most difficulty, we ran a post-hoc
procedure so we can analyze which portion results in a significant difference from the other
portions. Figure E.25 shows that the lowest mean value is maps for the Hudsonville’s students,
and the average rank for each portion.
Figure E.25. Post Hoc for Hudsonville and Ranks

47
School 8: Multicultural Academy
Figure E.26 shows the variability of Multicultural Academy’s students’ mean score for each
portion.
Figure E.26. Boxplots of Each Portion of the HSAG Exam for Grosse Point South
and independent samples. From Figure E.27, we see that the Levene’s test produces a test
statistic of 0.849 and a p-value of 0.493, so we conclude that there is significant evidence of
equal variances across the four portions of the HSAG Exam for the students of Multicultural
Academy.
Figure E.27. Levene’s Test SPSS Output for Grosse Point South

48
there is a difference in Multicultural Academy’s students’ mean section score between the four
Figure E.28. SPSS Output for the One-Way ANOVA Test for Multicultural Academy

other portions. Figure E.29 shows that the lowest mean value are essay and maps for the
Multicultural Academy students.
Figure E.29. Tukey HSD Test for Multicultural Academy

49
School 9: Okemos
Figure E.30 shows the variability of Black River’s students’ mean score for each portion.
Since there are a few extreme values, we suspect that our ANOVA assumptions will not be met.
Figure E.30. Boxplots of Each Portion of the HSAG Exam for Okemos
met. From Figure E.31, we see the test produces a test statistic 3.611 and a p-value of 0.014, so
we cannot conclude that there is significant evidence of equal variances across the four portions
of the HSAG Exam for the students of Okemos.
Figure E.31. Levene’s Test SPSS Output for Okemos
Since this assumption was NOT met, we cannot proceed with the One-Way ANOVA. We will be
conducting a Kruskal-Wallis Test instead.

50
χ2
(3) = 3.290 which gave us a p-value of 0.349. Therefore, there is not significant evidence to
show that there is a difference in Okemos’s students’ mean section score between the four
Figure E.32. Kruskal-Wallis Test for Okemos

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