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. Assumptions for a One-Way ANOVA:

1. Independent samples This assumption is met because each student’s total score on the HSAG

Exam from one year is independent of the other years.

2. Approximately Normal Populations 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.

 

Figure B.4. Skewness and Kurtosis SPSS Output for 2013  

 

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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.

 

 

Figure B.5. Skewness and Kurtosis SPSS Output for 2014

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 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 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

Since all three of the assumptions are met, we will proceed with the One-Way ANOVA.

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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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Assumptions for a One-Way ANOVA:

1. Independent samples This assumption is met because each student’s total score on the HSAG

Exam from one school is independent of the other schools.

2. Approximately Normal Populations 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

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 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. Assumptions for a One-Way ANOVA:

1. Independent samples This assumption is met because each focus student’s score on one portion

of the HSAG Exam is independent of the other portions.

2. Approximately Normal Populations 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 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 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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Since all three of the assumptions are met, we will proceed with the One-Way ANOVA.

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

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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

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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

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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 Since all three of the assumptions are met, we will proceed with the One-Way ANOVA.

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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

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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

We will only check for equal variances since we have a large sample to assume normality 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 Since all three of the assumptions are met, we will proceed with the One-Way ANOVA.

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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

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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

We will only check for equal variances since we have a large sample to assume normality 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 Since all three of the assumptions are met, we will proceed with the One-Way ANOVA.

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From Figure E.13 we see that our One-Way ANOVA test results in a test statistic of F = 3.102, which produces a p-value of 0.028. This means that there is significant evidence that there is a difference in Grosse Point South’s students’ mean section score between the four portions of the HSAG exam.

Figure E.13. SPSS Output for the One-Way ANOVA Test for Grosse Point South  

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.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

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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

We will only check for equal variances since we presume this assumption will not be 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

Since this assumption was NOT met, we cannot proceed with the One-Way ANOVA. We will be conducting a Kruskal-Wallis Test instead.

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From Figure E.17, we see that our Kruskal-Wallis test results in a test statistic of 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 portions of the HSAG exam.

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  

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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 Since all three of the assumptions are met, we will proceed with the One-Way ANOVA.

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From Figure E.21 we see that our One-Way ANOVA test results in a test statistic of 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

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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

We will only check for equal variances since we presume this assumption will not be 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

Since this assumption was NOT met, we cannot proceed with the One-Way ANOVA. We will be conducting a Kruskal-Wallis Test instead.

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From Figure E.24, we see that our Kruskal-Wallis test results in a test statistic of 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 portions of the HSAG exam.

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

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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

We will only check for equal variances since we have a large sample to assume normality 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 Since all three of the assumptions are met, we will proceed with the One-Way ANOVA.

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From Figure E.28 we see that our One-Way ANOVA test results in a test statistic of F = 8.177, which produces a p-value of 0.003. This means that there is significant evidence that there is a difference in Multicultural Academy’s students’ mean section score between the four portions of the HSAG exam.

Figure E.28. SPSS Output for the One-Way ANOVA Test for Multicultural 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.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

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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

We will only check for equal variances since we presume this assumption will not be 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.

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From Figure E.32, we see that our Kruskal-Wallis test results in a test statistic of 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 portions of the HSAG exam.

Figure E.32. Kruskal-Wallis Test for Okemos