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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
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
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
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.
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?
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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>
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
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
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
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
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
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