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Rosenstein 1 An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana State University May 8, 2010 A writing project submitted in partial fulfillment of the requirements for the degree Master of Science in Statistics

An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

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Page 1: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 1

An Assessment of Student Performance in

Statistics 216

Sabrina M. Rosenstein

Department of Mathematical Sciences Montana State University

May 8, 2010

A writing project submitted in partial fulfillment of the requirements for the degree

Master of Science in Statistics

Page 2: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 2

APPROVAL

of a writing project submitted by

Sabrina M. Rosenstein

This writing project has been read by the writing project director and has been found to be satisfactory regarding content, English usage, format, citations, bibliographic style, and consistency, and is ready for submission to the Statistics Faculty.

_________________ ___________________________________________

Date John J. Borkowski Writing Project Advisor

_________________ _________________________________________

Date Mark Greenwood Writing Project Coordinator

Page 3: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 3

Table of Contents

I. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 4

II. The Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 4

III. Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 5

IV. Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 5

V. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 18

VI. Recommendations for Further Analysis. . . . . . . . . . . . . . . . .Page 19

VII. Sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Page 20

VIII. Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Page21

Page 4: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 4

Introduction

Statistics 216, An Introduction to Statistics is an undergraduate course offered every

semester at Montana State University, Bozeman. Currently there are six hundred thirty eight

students enrolled in Statistics 216 during this spring 2010 semester. There are set prerequisites

that every student is recommended to meet before enrolling in Statistics 216. The set

prerequisites are that any student enrolling must have any one of the following: (a) ACT score of

23 or higher, (b) Math SAT score of 530 or higher, (c) a C- or better in any 100 level (or higher)

math course, or (d) a score of 3.5 or higher on the Math Placement Level Exam (MPLEX). These

have been the exact prerequisites for the past 12 semesters. The goal of this paper is to serve as

an exploratory data analysis assessing student performance in Statistics 216 and to examine

possible explanations for the observed student success, or lack thereof. This paper will serve as

a first step analysis exploring all current prerequisite requirements and student success or

failure over the past 10 years, detecting patterns and trends to later be explained with deeper

analysis by anyone wanting to investigate further.

Data The data that will be analyzed was collected by Montana State University, Bozeman and

compiled by Dr. Borkowski on all students enrolled in Statistics 216 during either the fall or

spring semesters over the past 10 years. The data consists of information collected on the 12,526

students enrolled in Statistics 216 from Fall Semester 2000 to the Spring Semester 2009

(nineteen semesters). The data contains information over many variables for each student, such

as the semester they were enrolled in Statistics 216, their final grade, quantitative SAT score,

ACT score, age when enrolled in Statistics 216, and their MPLEX score to name a few. For this

project the data was divided into several different subsets to create plots. First, all students with

who got an A, B, C, or D in a math class prior to 216 were extracted. If they earned these grades

in multiple courses, only the highest level math course taken was considered. Throughout the

paper they will be referred to as the Coursework Group. Then from the remaining group of

students, without coursework, those who met the prerequisite either with their SAT, ACT, or

MPLEX score were extracted. They will be referred to as the Tests Group.

Page 5: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 5

Methods This study used classical descriptive statistics to detect patterns and trends in the

performance of students taking statistics 216 over the past 10 years. Graphical methods were

used along with tables to observe relationships and detect trends. Barplots, side-by-side

boxplots, comparative barplots, cumulative frequency plots, and scatterplots were used to

display associations observed.

Results

Grade Frequency % Cum. Freq. Cum. %

A 1569 12.53 1569 12.53

B 3368 26.89 4937 39.41

C 3288 26.25 8225 65.66

D 1264 10.09 9489 75.75

F 1010 8.06 10499 83.82

W 2025 16.17 12526 100

Table 1: 216 Grade Distribution

Status Frequency % Cum. Freq. Cum.%

Fail 4301 34.33 4301 34.33

Pass 8227 65.67 12528 100

Table 2: Pass/Fail Status

To get a picture of the breakdown of the grade distribution of Statistics 216 students,

Tables 1 and 2 were created. Overall about twelve and a half percent of students are earning A’s

in Statistics 216, twenty seven percent are earning B’s, twenty six percent are receiving C’s, ten

percent are getting D’s, and eight percent are earning F’s in Statistics 216. On the whole, sixteen

percent are withdrawing from Statistics 216 with a W. Largely thirty four percent are failing

(meaning not passing – getting a D,F, or W) while sixty six percent are passing Statistics 216.

Based on this information some of the questions to be pursued in this paper are: Who is failing?

What is it about the students that are not passing 216 that is different from those who are?

Page 6: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 6

Figure 1: Barplot of Semester Enrolled in s216 * Proportion Not Passing

The barplot in Figure 1 is showing the proportion of students each semester that did not

pass Statistics 216. There is definitely an increasing trend over the earliest semesters. Back in

2000-2002 the proportion failing (meaning earning a D, F, or W in Statistics 216) was lower

than recent years. If last semester (Fall 2009) were removed, the increasing trend since 2002 is

not very strong; however, the average proportion not passing is still higher than it was in the

past. Hoping to provide possible explanations for such a rise, I investigated when certain

policies such as D/F reports, online homework, textbook changes, prerequisite changes,

withdraw policy changes, course supervision, and the proportion of adjuncts lecturing had

changed over the past 10 years hoping to provide possible explanations.

Figure 2: Barplot of Semester Enrolled in s216 * Proportion of Adjuncts Teaching

The barplot in Figure 2 is displaying the proportion of adjuncts teaching Statistics 216

each semester. There does not appear to be a strict increasing or decreasing pattern in the

proportion of adjuncts teaching each semester. Thus, there does not appear to be an association

between the proportion of adjuncts teaching and the proportion of students not passing

00F 01S 01F 02S 02F 03S 03F 04S 04F 05S 05F 06S 06F 07S 07F 08S 08F 09S 09F

Semester Enrolled * Proportion Not Passing

Semester enrolled in s216

Pro

por

tion

Not P

assi

ng

0.0

0.1

0.2

0.3

0.4

0.5

Fall SemesterSpring Semester

00F 01S 01F 02S 02F 03S 03F 04S 04F 05S 05F 06S 06F 07S 07F 08S 08F 09S 09F

Semester Enrolled in s216 * Proportion of Adjuncts Teaching

Semester Enrolled in s216

Pro

portio

n A

dju

nct

s

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Page 7: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 7

Statistics 216. Careful examination of textbook changes and course supervisors each semester

did not reveal any associations with student success in Statistics 216.

Investigating policy changes revealed that the creation of D/F reports and the

adjustment of the last day in the semester a student is permitted to withdraw from a course

with a W changed before 2000, and thus could not be associated with changes seen over the

length of this study. In fall 2004, the prerequisite for entering Statistics 216 was changed.

Before then, the course prerequisite for entering was passing Math 105 or higher. Starting that

fall, it was lowered to any 100 level math course. Students began entering Statistics 216 with

Math 103 or even Math 101. It was also found that online homework for all students enrolled in

Statistics 216 began in the spring 2005. Neither of these changes would explain the jump in

2003, but could potentially be the reason for the proportion of students failing remaining

higher than previous years.

To determine possible reasons why students were not passing Statistics 216 (e.g., were

the proportion of D’s, F’s or W’s rising?) separate barplots of the proportion of students getting

D’s, F’s and W’s for each semester were examined.

Figure 3: Barplot of Semester Enrolled in s216 * Proportion Received D in Course

The barplot in Figure 3 is examining the proportion of students who received D’s in

Statistics 216 each semester. There does not appear to be the same increasing pattern as seen in

the overall plot of the proportion of students not passing Statistics 216 each semester.

00F 01S 01F 02S 02F 03S 03F 04S 04F 05S 05F 06S 06F 07S 07F 08S 08F 09S 09F

Semester Enrolled * Proportion Received D in s216

Semester enrolled in s216

Pro

po

rtio

n s

21

6 g

rad

e=

D

0.0

00

.05

0.1

00

.15

Fall SemesterSpring Semester

Page 8: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 8

Figure 4: Barplot of Semester Enrolled in s216 * Proportion Received F in Course

Next, looking at a barplot of the proportion of students receiving F’s in Statistics 216

each semester (Figure 4) there does appear to be a slight increasing pattern over the earliest

semesters. If the most extreme semesters (Fall 2002 and Fall 2004) were removed, the trend

becomes more pronounced. However the pattern overall is not very strong unlike the overall

initial plot of the proportion of students not passing Statistics each semester.

Figure 5: Barplot of Semester Enrolled in s216 * Proportion Received W in Course Topped with # of Sections Offered

Examining the proportion of students withdrawing from Statistics 216 with a W each

semester (Figure 5) indicates a definite positive trend. It is clear that the proportion of students

withdrawing is increasing over time. This would explain the overall increasing trend in the plot

of the proportion of students not passing Statistics 216 each semester. The number on each bar

in Figure 5 is the number of sections of Statistics 216 that were offered each semester. They

appear to be rising with the proportion of students withdrawing with a W. Before Fall 2003, the

number of sections ranged from 13-15 sections of Statistics 216. After that time, a large jump

appeared in the number of sections offered. From Fall 2003-Fall 2009 the number of sections

00F 01S 01F 02S 02F 03S 03F 04S 04F 05S 05F 06S 06F 07S 07F 08S 08F 09S 09F

Semester Enrolled * Proportion Received F in s216

Semester enrolled in s216

Pro

portio

n s2

16 g

rade=

F

0.0

00.0

20.0

40.0

60.0

80.1

0

Fall SemesterSpring Semester

00F 01S 01F 02S 02F 03S 03F 04S 04F 05S 05F 06S 06F 07S 07F 08S 08F 09S 09F

Semester Enrolled * Proportion Received W in s216

Semester enrolled in s216

Pro

portio

n s

216 g

rade=W

0.0

00.0

50.1

00.1

50.2

00.2

50.3

00.3

5

14

13 14

1315

14

1716

19 17

19

18

2119

21

18

21

13

20Fall SemesterSpring SemesterFall SemesterSpring Semester

Page 9: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 9

varied from 17-21 sections with one exception in Spring 2009. There also seems to be a jump in

the proportion of students getting a W in Fall 2003 at the same time as a there was a large jump

in the number of students taking Statistics 216. Further studies could investigate if any

departments changed their policies, around this time. For example, did some departments start

requiring Statistics 216 that did not before?

Figure 6: Barplot of Prerequisite Course * Proportion Passing

Figure 6 is a barplot created from the Coursework Group. The courses are ordered

according to level of difficulty. The pink bar is depicting transfer students who got into Statistics

216 with a math course taken prior to 216 at another university. The number atop each bar is

the number of students in each category. It is apparent that a large number of students are

entering Statistics 216 after they have taken Math 170 and Math 105. The differences in the

proportions passing Statistics 216 are pretty similar for students who have taken Math 103-

Math 151. There is a jump in the success of students who have taken Math 170 and higher,

which is not unexpected as these are more challenging courses. This plot did show that there

was not much difference in the success rate of students who had taken Math 105 compared to

those who had only taken Math 103. However, students who had taken Math 101 did not have

as high of a rate of success. These differences may have added to the increasing trend seen in

the overall proportion of students not passing Statistics 216 each semester, after the lowering of

the course prerequisite to allow in students who had take Math 101 in Fall 2004. To examine

closer the exact grade distribution for students that have taken the more popular prerequisite

courses, Math 170, Math 105, and Math 160, individual comparative barplots of each course

were created. The barplots describe the Statistics 216 grade distribution for each grade received

in these courses.

a 065 b 085 d 101 e 103 f 130 g 150 h 105 i 131 j 149 k 151 l 110 m 170 n 160 o 175 p 181 trans

Prerequisite Course * Proportion Pass

Prerequisite Course

Pro

portio

n P

ass

0.0

0.2

0.4

0.6

0.8

1.0

25

55

142

48333 434

89561

16

76

15

1519 61472

608

1024

065 085 101 103 130 150 105 131 149 151 110 170 160 175 181 trans

Page 10: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 10

Figure 7: Comparative Barplot of Grade in Math 105 * Proportion Earning Grade in s216

The comparative barplot in Figure 7 is showing the Statistics 216 grade distribution for

students in the Coursework Group whose highest prior class is Math 105, for each grade received

in Math 105. For example, looking at the grade distribution for students who earned a C in

Math 105, approximately two percent earned an A in Statistics 216, fourteen percent got B’s, and

about thirty two percent earned a C in Statistics 216. Thus, approximately fifty percent of

students who earned a C in Math 105 passed Statistics 216. Overall the proportion of students

earning A’s and B’s in Statistics 216 are decreasing as their grade in Math 105 drops. The

proportion of students earning C’s, D’s, and F’s in Statistics 216 are increasing as their Math 105

grade drops.

Figure 8: Comparative Barplot of Grade in Math 170 * Proportion Earning Grade in s216

The comparative barplot in Figure 8 is showing the same thing as the plot in Figure 7,

only for Math 170 instead of Math 105. Approximately three percent of students who earned a C

in Math 170 earned an A in Statistics 216. Additionally, around twenty percent of students with

a C in Math 170 earned B’s in Statistics 216, and forty percent earned C’s. Thus, overall around

sixty three percent of students who earned C’s in Math 170 passed Statistics 216. As seen with

A B C D

Math 105 Grade * s216 Grade

Grade in 105

Pro

por

tion

0.0

0.1

0.2

0.3

0.4

0.5

0.6

216 Grade

ABCDFW

A B C D

Math 170 Grade * s216 Grade

Grade in 170

Pro

portio

n

0.0

0.1

0.2

0.3

0.4

0.5

0.6

216 Grade

ABCDFW

Page 11: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 11

students that took Math 105, the proportion of students earning A’s & B’s in Statistics 216 are

decreasing as the grade they received in Math 170 drops.

Figure 9: Comparative Barplot of Grade in Math 160 * Proportion Earning Grade in s216

The comparative barplot in Figure 9 is showing the same Statistics 216 grade distribution

as before, but for students whose prerequisite course is Math 160. The trend is very similar to

the trends observed in Figures 7 and 8.

065 085 101

103

130 150 105 131 149 151 110 170 160 175 181 Tran Sum

00F 0 3 0 8 3 18 85 4 0 11 4 116 42 5 36 92 427

01S 0 1 0 32 5 26 66 10 0 3 4 31 51 1 45 66 341

01F 0 2 0 33 3 7 30 4 0 7 2 27 24 2 25 74 240

02S 0 5 0 24 0 10 23 0 0 2 0 9 19 2 18 78 190

02F 0 6 0 10 0 4 12 0 0 3 2 11 9 1 9 90 157

03S 0 5 0 7 1 8 9 3 0 2 0 2 10 2 9 73 131

04F 0 4 0 43 2 20 70 2 0 10 1 142 35 7 41 67 444

05S 0 5 0 58 2 39 67 4 0 11 0 163 42 6 47 43 487

05F 0 1 1 50 5 39 72 1 0 6 0 200 53 8 59 42 537

06S 2 3 25 55 0 39 86 2 0 4 0 157 54 5 57 38 527

06F 1 2 21 35 2 32 65 2 1 2 0 144 55 4 59 30 458

07S 1 3 23 32 2 37 76 7 4 2 0 149 56 5 49 23 469

07F 3 0 18 23 2 42 56 6 5 0 0 114 51 6 46 31 403

08S 5 1 22 18 3 44 52 5 2 0 0 38 41 5 19 31 286

08F 8 3 13 16 1 31 35 6 3 3 0 27 25 4 26 33 234

09S 2 1 9 11 1 8 10 2 1 0 0 11 19 2 22 23 122

09F 3 5 10 4 0 7 8 2 0 0 0 6 8 3 6 24 86

Table 3: Semester * Prerequisite Course

A B C D

Math 160 Grade * s216 Grade

Grade in 160

Pro

portion

0.0

0.1

0.2

0.3

0.4

0.5

0.6

216 Grade

ABCDFW

Page 12: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 12

Table 3 is showing the number of students taking Statistics 216 each semester for each

course, for the students in the Coursework Group. The overall number of students enrolled in

Statistics 216 is consistently increasing over time. However, the table above is showing that the

number of students using a previous math course to meet the prerequisite for Statistics 216 has

plummeted. There was a steady rise in the number of students that had taken each course prior

to Statistics 216 from 2000-2005. Since then the number of students previously enrolled in

each course has been decreasing dramatically. Looking at Math 170, in 2005 two hundred

students enrolled in Statistics 216 has taken Math 170. Last semester (Fall 2009) only six

students did so. A future study might consider further investigation. It is possible a department

may have stopped requiring its students to take Math 170 as well as Statistics 216. It could also

be that students are taking Statistics 216 earlier in their academic studies, before they have

taken any math courses, or have only received F’s or W’s in the math classes they have taken.

Whatever the cause, it is clear that students in recent years are not using math courses to meet

the prerequisite for Statistics 216 like they were in the past.

Figure 10: Scatterplot of SAT Score * Proportion Passing Figure 11: Scatterplot of Binned SAT Scores * Proportion Passing

Figures 10 and 11 were created from the Tests Group. They are scatterplots displaying

SAT scores by the proportion of students with each SAT score that passed Statistics 216. The red

line in Figure 10 is showing the current Statistics 216 SAT prerequisite, an SAT score of 530 or

higher. There is a definite increasing trend seen in both plots, which is good, suggesting that

students with higher SAT scores have higher rates of success in Statistics 216. There did not

seem to be a large difference in the success of students with SAT scores near 530, suggesting

raising the SAT prerequisite for Statistics 216 slightly may not have much effect on student’s

success rate.

400 500 600 700 800

0.4

0.6

0.8

1.0

SAT Score * Proportion Pass

SAT Score

Pro

por

tion

Pas

sed

0.5

0.6

0.7

0.8

SAT Score * Proportion Pass

SAT Score

Pro

portio

n P

ass

ed

<490 490-520 530-560 570-600 610-640 650-680 >680

Page 13: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 13

Figure 12: Cumulative Plot of SAT Score * Proportion Not Passing

Figure 12 is a plot of SAT scores by the cumulative proportion of student’s failing. The

green line is describing the Tests Group. The blue line is describing the Coursework Group. The

red line is the current Statistics 216 prerequisite, an SAT score of 530 or higher. For students

who did not have any previous math coursework, approximately twenty one percent of those

with SAT scores of 530 or higher did not pass Statistics 216. For students who did have prior

coursework, about twenty three percent with SAT scores of 530 or higher did not pass. For both

groups, students with higher SAT scores had higher levels of success in Statistics 216.

Figure 13: Boxplot of s216 Grade * SAT Score

The boxplots in figure 13 are describing the distribution of SAT scores for each grade

received by students in the Tests Group. There is a lot of variability in SAT scores for each grade

and not much difference in the SAT scores of students who earned C’s, D’s, F’s, and W’s in

Statistics 216. Students earning A’s did have higher SAT scores overall, but quite a few students

400 500 600 700 8000

.00

0.0

50

.10

0.1

50

.20

0.2

50

.30

Sat Score * Cumulative Proportion Fail

Sat Score

Cu

mu

lativ

e P

rop

ort

ion

Fa

il

SAT,ACT,MPLEX=prereqCourse Work=prereq

A B C D F W

400

500

600

700

800

s216 Grade * SAT Score

s216 Grade

SA

T S

core

Page 14: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 14

with high SAT scores did not do well in 216. In fact all the median SAT scores for each grade

received were well above the prerequisite score of 530, thus more than half of the students not

passing Statistics 216 met the SAT prerequisite for entering the course.

Figure 14: Scatterplot of ACT Score * Proportion Passing Figure 15: Scatterplot of ACT Score * Proportion Passing

The plots in Figures 14 and 15 are describing the Tests Group. They are scatterplots of

student’s ACT score by the proportion of students who passed Statistics 216. The red line in

figure 14 is showing the current Statistics 216 prerequisite, an ACT score of 23. The trend

observed is very similar to the one seen on the same plot of student’s SAT scores. There is

definitely a positive trend seen in both plots. Thus students with higher ACT scores are having

higher rates of success in Statistics 216.

Figure 16: Cumulative Plot of ACT Score * Proportion Not Passing

Figure 16 above is a plot of student’s ACT scores and the cumulative proportion of

students not passing Statistics 216. The green line is again describing the Tests Group and the

15 20 25 30 35

0.0

0.2

0.4

0.6

0.8

1.0

ACT Score * Proportion Pass

ACT Score

Pro

por

tion

Pa

sse

d

0.4

0.5

0.6

0.7

0.8

ACT Score * Proportion Pass

ACT Score

Pro

portio

n P

ass

ed

<17 17-19 20-22 23-25 26-28 29-31 >31

15 20 25 30 35

0.0

00.0

50.

10

0.1

50.2

00.2

50.3

00.

35

ACT Score * Cumulative Proportion Not Passing

ACT Score

Cum

ula

tive P

ropor

tion N

ot P

ass

ing

SAT,ACT,MPLEX=prereqCourse Work=prereq

Page 15: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 15

blue line is describing the Coursework Group. The red line is the current Statistics 216

prerequisite- an ACT score of 23 or higher. Once again a very similar trend to the cumulative

SAT plot was seen, with even identical percents failing at the prerequisite level or higher for the

tests group and the coursework group. The spike in the proportion of students failing right

around an ACT score of 34 is unexpected and likely due to the small number of students with an

ACT score of 34 or higher.

Figure 17: Boxplot of s216 Grade * ACT Score

Figure 17 is a plot of side-by-side boxplots of the distribution of ACT scores for each

grade received in Statistics 216. These are displaying trends very similar to the ones seen in the

SAT boxplots, with the variability and differences across grades. Again the median ACT score

for each grade is well above the prerequisite score of 23. Thus more than half of the people not

passing 216 met the ACT prerequisite.

Figure 18: Scatterplot of MPLEX Score * Proportion Passing

A B C D F W

152

025

30

35

s216 Grade * ACT Score

s216 Grade

AC

T S

core

1 2 3 4 5

0.6

50

.70

0.7

50

.80

MPLEX Score * Proportion Pass

MPLEX Score

Pro

po

rtio

n P

asse

d

Page 16: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 16

Figure 18 is a scatterplot of students MPLEX score by the proportion of students passing

Statistics 216. The red line is again the current Statistics 216 prerequisite, an MPLEX score of

3.5 or higher. Students who earned a 3 on the MPLEX performed significantly better than

students who scored a 2 on the MPLEX. The downward trend after a score of 3 was surprising.

It was expected that student success would rise with an increasing MPLEX score, as seen with

SAT and ACT scores.

Figure 19: Scatterplot of # of Previous Semesters Enrolled in s216 * Proportion Not Passing

The scatterplot in Figure 19 is portraying the relationship between the number of

previous semesters a student was enrolled in Statistics 216 and the proportion of student’s not

passing Statistics 216. As the number of previous semesters enrolled rises, so does the

proportion not passing. It appears that students who have been enrolled in Statistics 216 for 5

or 6 previous semesters do not have high success in Statistics 216 on their 5th/6th semester

enrolled.

Figure 20: Scatterplot of Age Enrolled in s216 * Proportion Not Passing

The scatterplot in Figure 20 above was created based on all students, showing the age

when enrolled in Statistics 216 by the proportion of students not passing. Ninety percent of all

0 1 2 3 4 5 6

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

# of Previous Semesters Enrolled in s216 * Proportion Not Passing

# of Previous Semesters Enrolled s216

Pro

portio

n N

ot P

ass

ing

18 19 20 21 22 23 24 25

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Age Enrolled in s216 * Proportion Not Passing

Age Enrolled in s216

Pro

porti

on N

ot P

ass

ing

Page 17: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 17

students enrolled in 216 were between the ages of eighteen and twenty five, so this graph was

focused on those ages. There is a definite trend in this plot. As students get older, they tend to

perform worse in Statistics 216. This is suggesting that freshmen taking Statistics 216 early in

their academic studies are overall performing better than students putting it off till they are

older. About twenty seven percent of eighteen year olds did not pass Statistics 216, while forty

two percent of twenty five year olds did not pass.

Figure 21: Comparative Barplot of Age when Enrolled in s216 * Proportion Earning Grade in s216

To determine exactly how students are not passing Statistics 216 as they get older (are

more withdrawing, getting D’s, or getting F’s) the comparative barplot in figure 21 was created.

It displays students age when enrolled, binned into ranges, and the distribution of their grades.

One very clear trend is that the proportion of students withdrawing with a W from Statistics 216

definitely keeps rising as students get older.

<=18 19 20 21-22 23-29 >=30

Age * 216 Grade

Age

Proportion

0.0

0.1

0.2

0.3

0.4

0.5

216 Grade

ABCDFW

Page 18: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 18

Conclusion Using classical descriptive statistics to detect patterns and trends in the performance of

students taking statistics 216 over the past 10 years showed that overall, the proportion of

students each semester that did not pass Statistics 216 is rising. The average proportion of

students not passing since 2003 is higher than it was from 2000-2002. The cause for the rise

was found to be an increase in the proportion of students withdrawing from Statistics 216 with a

W. The overall number of students enrolled in Statistics 216 is consistently increasing over

time. However, the number of students using a previous math course to meet the prerequisite

for Statistics 216 has plummeted. Furthermore, while there was a steady rise in the number of

students that had taken each course prior to Statistics 216 from 2000-2005, since then the

number of students previously enrolled in each course has been decreasing dramatically.

Examining student success in Statistics 216 by their previous coursework, it was

discovered that there is not much difference in the success rate of students who had taken Math

105 prior to Statistics 216 compared to those who had only taken Math 103. However, students

who had taken Math 101 did not have as high of a rate of success. These differences may have

added to the increasing trend seen in the overall proportion of students not passing Statistics

216 each semester, after the lowering of the course prerequisite to allow in students who had

take Math 101 in Fall 2004. There also seemed to be a jump in the proportion of students

getting a W in Fall 2003 at the same time as a there was a large jump in the number of students

taking Statistics 216.

Close examination of plots of students SAT score and ACT score versus their grade

earned in Statistics 216 revealed that there was not much difference in the SAT and ACT scores

of students who earned C’s, D’s, F’s, and W’s in Statistics 216. Additionally, the median SAT and

ACT scores for each grade received in Statistics 216 were well above the prerequisite scores.

Thus more than half of the students not passing Statistics 216 met the SAT and ACT

prerequisites for entering the course. Plots of SAT and ACT score by the proportion of students

passing Statistics 216 showed definite positive trends suggesting students with higher SAT and

ACT scores are having higher rates of success in Statistics 216.

It was also found that students who earned a 3 on the MPLEX performed significantly

better than students who scored a 2 on the MPLEX. However, the observed downward trend

after a score of 3 was surprising, as it was expected that student success would rise with an

increasing MPLEX score, as seen with SAT and ACT scores. Furthermore, as the number of

previous semesters enrolled rises, so does the proportion not passing. It appears that students

who have been enrolled in Statistics 216 for 5 or 6 previous semesters do not have high success

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Rosenstein 19

in Statistics 216 on their 5th/6th semester enrolled. Additionally, as students get older, they tend

to perform worse in Statistics 216. This is suggesting that freshmen taking Statistics 216 early in

their academic studies are overall performing better than students putting it off till they are

older. About twenty seven percent of eighteen year olds did not pass Statistics 216, while forty

two percent of twenty five year olds did not pass. This decrease in the proportion passing

Statistics 216 as they get older is due the fact that the proportion of students withdrawing with a

W from Statistics 216 keeps rising as students get older. Again, this is simply a first step

analysis, all patterns and trends observed will need to later be explained with deeper analysis by

anyone wanting to investigate further.

Recommendations for Further Analysis This project was just a first step analysis for anyone wanting to investigate further.

Deeper exploration of all preliminary results made here are necessary to explain all patterns and

trends. One thing not included in this dataset are the summer sections of Statistics 216. It

would be interesting to see what is going on during the summer. What is it about students that

take 216 during the summer that is different from students enrolled during the fall or spring?

How many students are repeating the course? How many are withdrawing? How many meet

the prerequisites?

It may eventually be useful to build some type of predictive model to predict student’s

grade in Statistics 216. This would help isolate what are significant predictors of success in

Statistics 216.

Ultimately, this study might be useful as a guide to be extended to other math courses

offered here at MSU, such as Math 105, or Math 181 with large enrollment rates.

Page 20: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 20

Sources Cody, Ronald P., Smith, Jeffrey K. “Applied Statistics and the SAS Programming

Language, Fifth Edition”, Pearson Prentice Hall, Pearson Education, Inc., Upper Saddle

River, NJ 2006.

Crawley, Michael J. “The R Book”, John Wiley & Sons Ltd, The Atrium, England, 2007.

Friendly, Michael. “Visualizing Categorical Data”, SAS Institute Inc., Cary, NC, USA,

2000.

Office of Planning and Analysis, Montana State University, Bozeman. “Retention and

Graduation Rates”. Montana State University-Bozeman, Profile of First-time, Full-

time, Degree-Seeking Freshmen, All. 13 February 2010.<

http://www.montana.edu/opa/facts/FroshRatesAll.html>

Page 21: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 21

Appendix

Prereq Course Frequency % Cum. Freq Cum. %

065 25 0.2 25 0.20

085 55 0.44 80 0.64

101 142 1.13 222 1.77

103 483 3.85 705 5.63

130 33 0.26 738 5.89

150 434 3.46 1172 9.350

105 895 7.14 2067 16.50

131 61 0.49 2128 16.98

149 16 0.13 2144 17.11

151 76 0.61 2220 17.72

110 15 0.12 2235 17.84

170 1519 12.12 3754 29.96

160 615 4.91 4369 34.87

No 3528 28.16 7897 63.02

175 72 0.57 7969 63.60

181 608 4.85 8577 68.45

Transfer 1025 8.18 9602 76.63

Table A1: Prerequisite Course

Page 22: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 22

Freq

Column % <=18 19 20 21-22 23-30 >30

Total

A 120

19.51%

433

16.38%

395

12.61%

310

9.45%

231

10.11%

80

14.06% 1569

B 188

30.57%

821

31.06%

918

29.30%

787

23.98%

509

22.29%

145

25.48% 3368

C 141

22.93%

632

23.91%

870

27.77%

951

28.98%

578

25.31%

116

20.39% 3288

D 47

7.64%

221

8.36%

309

9.86%

376

11.46%

253

11.08%

58

10.19%

1264

F 44

7.15%

151

5.71%

196

6.26%

283

8.62%

290

12.70%

46

8.08%

1010

P 0

0.00%

0

0.00%

0

0.00%

1

0.03%

0

0.00%

1

0.18%

2

W 75

12.20%

385

14.57%

445

14.20%

574

17.49%

423

18.52%

123

21.62%

2025

Total 615 2643 3133 3282 2284 569 12526

Table A2: Age Enrolled in s216 * Grade in s216

Freq

Column %

<=18

19

20

21-22

23-30

>30

Total

Fail 166

26.99%

759

28.70%

950

30.32%

1233

37.57%

966

42.29%

227

39.89%

4301

Pass 449

73.01%

1886

71.30%

2183

69.68%

2049

62.43%

1318

57.71%

342

60.11%

8227

Total 615 2645 3133 3282 2284 569 12528

Table A3: Age Enrolled in s216* Pass/Fail Status

Page 23: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 23

Freq

Row % A B C D F P W Total

065 2

8.00%

2

8.00%

5

20.00%

2

8.00%

2

8.00%

0

0.00%

12

48.00% 25

085 1

1.82%

13

23.64%

11

20.00%

8

14.55%

4

7.27%

0

0.00%

18

32.73%

55

101 0

0.00%

11

7.75%

38

26.76%

28

19.72%

15

10.56%

0

0.00%

50

35.21% 142

103 18

3.73%

81

16.77%

150

31.06%

57

11.80%

62

11.80%

0

0.00%

115

23.81% 483

130 0

0.00%

11

33.33%

7

21.21%

1

3.03%

4

12.12%

0

0.00%

10

30.30% 33

150 30

6.91%

84

19.35%

113

26.04%

48

11.06%

29

6.68%

0

0.00%

130

29.95% 434

105 41

4.58%

203

22.68%

270

30.17%

125

13.97%

76

8.49%

0

0.00%

180

20.11% 895

131 7

11.48%

17

27.87%

13

21.31%

9

14.75%

4

6.56%

0

0.00%

11

18.03%

61

149 0

0.00%

6

37.50%

5

31.25%

1

6.25%

1

6.25%

0

0.00%

3

18.75% 16

151 5

6.58%

15

19.74%

21

27.63%

7

9.21%

11

14.47%

0

0.00%

17

22.37% 76

110 3

20.00%

6

40.00%

1

6.67%

2

13.33%

1

6.67%

0

0.00%

2

13.33% 15

170 192

12.64%

494

32.52%

466

30.68%

127

8.36%

68

4.48%

0

0.00%

172

11.32% 1519

160 58

9.45%

180

29.32%

212

34.53%

56

9.12%

46

7.49%

0

0.00%

62

10.10% 614

175 11

15.28%

17

23.61%

21

29.17%

15

20.83%

4

5.56%

0

0.00%

4

5.56% 72

181 161

26.48%

189

31.09%

134

22.04%

45

7.40%

32

5.26%

0

0.00%

47

7.73% 608

Trans 104

10.16%

236

23.05%

262

25.59%

135

13.18%

118

11.52%

0

0.00%

169

16.50% 1024

Page 24: An Assessment of Student Performance in Statistics 216 · An Assessment of Student Performance in Statistics 216 Sabrina M. Rosenstein Department of Mathematical Sciences Montana

Rosenstein 24

Yes 636

21.72%

997

34.05%

631

21.55%

198

6.76%

166

5.67%

1

0.03%

299

10.21% 2928

No 300

8.51%

806

22.86%

928

26.32%

400

11.34%

367

10.41%

1

0.03%

724

20.53% 3526

Total 1569 3368 3288 1264 1010 2 2025 12526

Table A4: Grade in s216 * Prerequisite Course

Frequency

Row % Fail Pass Total

065 16

64.00%

9

36.00% 25

085 30

54.55%

25

45.45% 55

101 93

65.49%

49

34.51% 142

103 234

48.45%

249

51.55%

483

130 15

45.45%

18

54.55% 33

150 207

47.70%

227

52.30% 434

105 381

42.57%

514

57.43% 895

131 24

39.34%

37

60.66% 61

149 5

31.25%

11

68.75% 16

151 35

46.05%

41

53.95% 76

110 5

33.33%

10

66.67%

15

170 367

24.16%

1152

75.84% 1519

160 164

26.71%

450

73.29% 614

175 23

31.94%

49

68.06% 72

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Rosenstein 25

181 124

20.39%

484

79.61% 608

Transfer 423

41.27%

602

58.73% 1025

Yes 663

22.64%

2265

77.36% 2928

No 1492

42.30%

2035

75.70% 3527

Total 4301 8227 12528

Table A5: Pass/Fail Status * Prerequisite Course

Freq

Column % 1 2 3

4

5 6 Total

A 694

12.68%

42

3.94%

4

2.03%

1

2.63%

0

0.00%

0

0.00% 741

B 1502

27.44%

185

17.34%

25

12.69%

3

7.89%

0

0.00%

0

0.00% 1715

C 1430

26.13%

339

31.77%

68

34.52%

11

28.95%

1

8.33%

0

0.00% 1849

D 542

9.90%

154

14.43%

27

13.71%

0

0.00%

0

0.00%

0

0.00%

723

F 423

7.73%

133

12.46%

38

19.29%

7

18.42%

4

33.33%

0

0.00% 605

P 2

0.04%

0

0.00%

0

0.00%

0

0.00%

0

0.00%

0

0.00% 2

W 880

16.08%

214

20.06%

35

17.77%

16

42.11%

7

58.33%

3

100.00% 1155

Total 5473 1067 197 38 12 3 6790

Table A6: Number of Previous Semesters Enrolled * Grade in s216

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Rosenstein 26

Freq

Column %

1

2

3

4

5

6

Total

Fail 1846

33.72%

501

46.95%

100

50.76%

23

60.53%

11

91.67%

3

100.00% 2484

Pass 3628

66.28%

566

53.05%

97

49.24%

15

39.47%

1

8.33%

0

0.00% 4307

Total 5474 1067 197 38 12 3 6791

Table A7: Number of Previous Semesters Enrolled * Pass/Fail Status

# MPLEX

Attempts

Frequency

Percent

Cumulative

Frequency

Cumulative

Percent

0 8816 70.36 8816 70.36

1 2274 18.15 11090 88.51

2 816 6.51 11906 95.02

3 326 2.6 12232 97.62

4 160 1.28 12392 98.90

5 89 0.71 12481 99.61

6 30 0.24 12511 99.85

7 8 0.06 12519 99.91

8 2 0.02 12521 99.93

9 3 0.02 12524 99.95

10 2 0.02 12526 99.97

13 2 0.02 12528 99.98

15 2 0.02 12530 100.00

Table A8: Number of MPLEX Attempts