On the Time to Graduation and Graduation Rates in a Business School
An Operations Management Perspective
Bringing an Immediate Real-Life Challenge of Undergraduate Students
into the Operations Management and Statistics Classrooms
Ardavan Asef-Vaziri
Systems and Operations Management
College of Business and Economics
California State University, Northridge
Operations Management Course. Customers have certain expectations about the products they
buy or the services they render. These expectations can be physical, such as comfort,
convenience, and safety; psychological, such as relaxation and peace of mind; social, such as
feeding the poor, and spiritual, such as carrying a less materialistic load. These expectations
should be met within a budget. Operations, Marketing, and Finance are the three primary
functions of business organizations. Operations management focuses on how managers can
design and operate processes in business settings with discrete flow units. Examples of discrete
flow include; flow of cars in an assembly plant, flow of customers in a branch of a bank, flow of
patients in a Medical Center, flow of cash in an order fulfillment process, and flow of
undergraduate students during their program at an academic institute. In all these systems,
Inputs (natural resources, semi-finished goods, products, customers, patients, students, and
cash) in the form of flow units flow through a set of Processes (formed by a network of Activities
and Buffers) utilize Human Resources and Capital Resources (such as equipment, buildings,
tools) to become a desired Outputs. The reason for the being of operations management is
structuring (designing), managing, and improving processes to achieve the desired output as
defined in a four-dimensional space of quality, cost, time, and variety (adopted from[1]).
One of the most binding constraints of business school students, from the time they are
admitted to college as raw material from high school to the time they graduate and leave college
as the final product, is their low quantitative and analytical skills. Believing that managers cannot
go far if their quantitative and analytical capabilities are below a threshold. One of the key
features of operations management courses is to improve the analytical capabilities and
spreadsheet modeling skills of these business school students [2]. Other contributions of the
operations management courses and their relative importance can be depicted in a figure
similar to Figure 1.
Figure 1. Specific Features of Operations Management Courses.
Omni channels [3] of the supply chain of course delivery systems can be envisioned as
traditional, on-line, flipped, and distributed. In a distributed channel, the lectures are delivered
online, problem solving and trouble-shooting tasks are handled by teaching assistants who each
support a small group of students living in the same neighborhood. The problem-solving and
trouble-shooting sessions will take place in a coffee shop, or a park, etc. One of the competing
channels is the flipped classroom. By delivering lectures on the basic concepts using the screen
capture technology, students can learn the material at a time and location of their choice, which
allows them to pause, rewind, or fast forward professors’ lectures as needed. The class time is
no longer spent on teaching basic concepts, but rather on more value-added activities, such as
problem solving, answering questions, creative-thinking, systems-thinking, as well as real
world applications and discussions, potential collaborative exercises such as case studies, and
virtual-world applications such as web-based simulation games [2]. Benefits of a flipped
classroom may be observed in Figure 2.
Figure 2. Traditional Lectures vs. Interactive Engagement [3].
A flipped classroom includes components of both an online and a traditional course. It is an
online course because its online components must compete with the best of the online courses.
A flipped classroom is also a traditional course because not even a single class session is
purposely cancelled while all the lectures are delivered online [2]. A network of resources and
learning processes reinforces this core concept, Figure 3, ensuring a smooth, lean, and
synchronized course delivery system [2].
Figure 3. Resources and learning processes of a flipped classroom.
The main objectives of an operations management course may be summarized as follows:
1. Creating a smooth flow.
2. Understanding Trade-offs
3. Reducing Variability
4. Balancing inventory buffer, capacity buffer, and time buffer.
5. Aligning the process competency with product attributes
Time to Graduation (TtG) and Retention Rate (RR).
In an effort to better prepare and assist students, the California State University (CSU) system
has established a plan to remove obstacles to receiving a baccalaureate degree. The CSU
Graduation Initiative 2025 (GI-2025) was launched in January 2015 with a clear goal: to increase
graduation rates for about half a million students across 23 campuses. The initiative established
a series of objectives, which include increasing the 4-year and 6-year GRs to 40% and 70%,
respectively [4, 5, 6], expecting to bring the total number of CSU graduates to more than one
million between 2015 and 2025.
In this manuscript, we not only approach GI-2025 from an Operations Management and
Business Analytics (OM&BA) perspective, and provide model-based, student-centered analysis,
but also replace the problems of these two courses, by examples related to Time to Graduation
(TtG) and Retention Rate (RR) in GI-2015. We replace some of the existing examples, which
many not have a close link to the real life of our students, with examples that are related to the
immediate real-life of the students on TtG and RR. Analysis of the student’s real life situations
could have profound impact on learning processes (see for example [7]).
We will study the past 16-year’s performance of first-time-freshmen students (FTF) and firsttime-transfer students (FTT) at DN-CBE on TtG and GR dimensions. We will implement
prescriptive quantitative tools and software to provide insight in order to envision and establish
the governing constraints. Descriptive statistics such as categorical and numerical histograms,
measures of centralization, coefficients of variations, percentiles and quartiles, 5-number boxplots, cross tabulations, goodness of fit-to-known probability distributions, correlation analysis,
confidence intervals, test of hypothesis, and analysis of variance will be prepared to understand
the past.
Process View of Undergraduate Studies.
Prepare a process graph containing five elements of input, value added processes, non-value
added processes, human and capital resources, and information infrastructure for
undergraduate study.
In operations management, everything is viewed as a process, and we believe every process can
be improved. The five components of Process View are: (1) inputs, (2) outputs, (3) human
resources and capital resources, a (4) network of value added/non-value added activities and
buffers, and an (5) information structure and value system. Inputs can be tangible or intangible,
natural or processed resources, parts and components, energy, data, customers, cash, etc.
Outputs can be tangible or intangible items such as products, byproducts, energy, information,
served customers, cash, relief, etc., that flow from the system back into the environment. In
process flow mapping (process blueprinting), material flow is shown by solid lines, and
information flow is shown by dashed lines. When inputs pass through the network, they are
referred to as flow units. When they leave the system, they are referred to as output. Value
added activities are the activities required to transform an input one step closer to its output
form. They are shown by a rectangle. Non-value added activities, primarily buffers, storages,
and waiting lines, are shown by triangles. Not all waiting times are non-value added, for
example, the aging of cheese or the time required for hardening concrete are examples of value
added waiting times.
Like any other production and service system, the undergraduate studies can be presented as a
process. Inputs are the FTF and FTT from community colleges, and outputs are graduates,
dropouts, and students who transfer to other institutes. There are human resources, such as
professors, teacher assistants, advisors, and administrators. There are also capital resources
such as classrooms, libraries, hardware, software, recreation areas, etc. There is a network of
value added and non-value added activities. These include learning processes inside the
classrooms and over the internet, TA hours, waiting lines in front of the offices of
administrators, professors, and teaching assistants. There is a value system, such as being a
student center learning environment. Finally, there is information infrastructure, such as
grading, transcripts, etc. just like our grading system and our transcripts. This process is
pictorially represented in Figure 3.
Figure 4. Pictorial representation of the undergraduate study.
Process Competencies. As illustrated in Figure 4, any system should have a reasonable
financial and value-chain performance. In this direction, the institute should satisfy its
customers, as well as its stakeholders. It should understand the perceptions and expectations.
All manufacturing and service systems, including an educational institute, offer a customer
value proposition (CVP). The CVP is defined in the four-dimensional space of cost, quality,
time, and variety to match with the product attributes expected by the customers. The process
competencies - cost, quality, flow-time, and flexibility - are then aligned with the CVP and
product attributes.
Figure 5. Strategy, Customer Value Proposition, Process Competencies.
We first look at cost at our institute, and then we extend the analysis to quality-to-cost. We
continue to include time and variety dimension.
Cost-Quality Efficient Frontier.
Over a period of 7 years, we collected a set of data, where we asked about a thousand students
what their perception is about Stanford, Berkeley, USC, Pepperdine, Lutheran University, and
CSUN. The average scores in a scope of 1 to 7 are shown on the Y-axis in Figure 5. Our institute
was not found in a weak position. Furthermore, the score of our institute was better when
appraised by students of other institutes as compared to appraisals by our own students. The
total tuition cost can be shown on the horizontal axis, but we will remain more consistent if the
horizontal axis represents 1/cost. This is because, on both axes we like to represent being
farther from the origin, representing a better situation [1]. Unlike the subjective and qualitative
judgement on the Y-axis, identifying the position of the institutes on the X-axis is quantitative
and straightforward. Given the tuition of the least and most expensive institutes in this set are
$6,000 and $42,000, respectively. Therefore, cost efficiencies (1/cost) are 1 for the least and 1/7
for the most expensive institute, respectively. In the quality-cost graph, institute L has a below
average quality and an average cost efficiency. Firms not on an efficient frontier can improve on
both dimensions of cost efficiency and quality. Institute B is an excellent university on the
efficient frontier of cost and quality. Institute S, also on the efficient frontier; a very high cost
institution, and at the same time, an extremely high quality institution. Firms on the efficient
frontier can improve quality only if they sacrifice cost efficiency, and vice versa. Firms on the
efficient frontier can improve on both dimensions only in case of outbreaks in their technoeconomical eco-system. The data collected from the students and faculty of other institutes,
indicates that, in quality dimension, they see our institute in a better light than what we see
ourselves. N is somewhere here.
Figure 6. Quality and Cost Efficient Frontier.
Now, for the purpose of schematic representation, let’s see how we can migrate from the twodimensional space of quality-cost to the one-dimensional space of quality-to-cost. Note that the
vertical axis represents quality, and the horizontal axis is K/cost or K (1/cost). Ignoring K, the
multiplication of the Y-side by the X- side is represented by the area of the corresponding
rectangle, which is the quality-to-cost of the corresponding institute. As we can see, our institute
represents a relatively large rectangle close to the rectangle of esteemed institute B. CSUN is
performing great in quality-to-cost dimension.
In order for the College of Business and Economics to be successful it needs to have a
reasonable value chain and financial performance. The good value chain performance, will lead
to student success, and our stakeholders’ satisfaction. We have proposed a value to our
students. We need align our resources and learning processes, and in general, process
competencies, with our student value proposition, to be able to fulfill perceptions and
expectations of our students as well as our stakeholders. In that case, we can compete in a fourdimensional space of: quality of education, tuition, number and variety of classes and courses,
and time to graduation, where time to graduation by itself is a function of head-count and the
number of incoming students, and the number of graduates. Input and output, according to the
Little’s Law, throughput times flow time is equal to inventory. Average of incoming and
graduates each year times the time to graduation is equal to the headcount of students.
Table 1. 16-year data on incoming students, headcount (population), and graduates.
Year
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
Incoming
IN-FTF IN-FTT IN-FTA
548
879
1,427
582
765
1,347
623
750
1,373
536
709
1,245
659
987
1,646
674
1,028
1,702
701
1,042
1,743
791
935
1,726
624
938
1,562
693
1,068
1,761
676
1,101
1,777
548
846
1,394
746
1,169
1,915
785
1,278
2,063
783
1,327
2,110
601
1,061
1,662
Headcount
HC-F HC-T HC-A
2,232 3,534 5,766
2,383 3,550 5,933
2,519 3,423 5,942
2,550 3,126 5,676
2,729 3,474 6,203
2,954 3,693 6,647
3,009 3,730 6,739
3,036 3,659 6,695
2,701 3,429 6,130
2,717 3,231 5,948
2,723 3,187 5,910
2,705 3,011 5,716
2,946 3,025 5,971
3,281 3,183 6,464
3,468 3,504 6,972
3,411 3,467 6,878
GR-F
229
228
311
305
327
335
393
413
425
410
443
384
432
401
521
516
Graduates
GR-T GR-A
802
1,031
866
1,094
949
1,260
971
1,276
1,009
1,336
988
1,323
1,053
1,446
1,126
1,539
1,010
1,435
982
1,392
1,052
1,495
972
1,356
999
1,431
886
1,287
818
1,339
1,006
1,522
FTF: first time freshmen student, FTT: first time transfer student, FTA: total FTF+FTT, IN: incoming, HC: headcount
(population), GR: Graduates. Source: Institutional Research, California State University. The excel file is available at
here.
Table 1 shows 16-years performance of our college.
Prepare the main descriptive statistics for Table 1 in Table 2. Also, include the 95% confidence
interval.
Note that for Table 2, we have first used the descriptive statistics of the Data Analysis Add-ins
as a template. We then have replaced all cells but their corresponding functions in excel. The
reader may refer to FORMULA TEXT in the accompanying excel file. This replacement has two
benefits: (i) if there is a change in the original table, there is no need to reproduce the descriptive
statistics table, and (ii) we can copy the cells to the right to compute descriptive statistics for INFTT, IN-FTA, etc. For 95% confidence interval, we have used the excel CONFIDENCE function.
Since the standard deviation is not known, CONFIDENCE.T was used.
Table 2. Descriptive Statistics. Incoming, Head-Count, Graduates 2001-2016.
IN-FTF
IN-FTT
IN-FTA
HC-F
661
22
667
86.1
0.13
7415
-1.12
0.13
255
536
791
16
46
707
615
993
45
1,008
179.3
0.18
32134
-0.47
0.19
618
709
1,327
16
96
1,088
897
1,653
63
1,682
252.1
0.15
63569
-0.58
0.18
865
1,245
2,110
16
134
1,788
1,519
2,835
88
2,726
351.2
0.12
123340
-0.40
0.30
1,236
2,232
3,468
16
187
3,022
2,648
Mean
Standard Error
Median
Standard Deviation
CV
Sample Variance
Kurtosis
Skewness
Range
Minimum
Maximum
Count
95% CI
UCL
LCL
HC-T
HC-A
GR-F
GR-T
GR-A
3,389 6,224
58
110
3,448 6,051
232.5 439.0
0.07
0.07
54039 192747
-1.13
-1.34
-0.27
0.47
719
1,296
3,011 5,676
3,730 6,972
16
16
124
234
3,513 6,458
3,265 5,990
380
21
397
86.0
0.23
7387
-0.27
-0.23
293
228
521
16
46
425
334
968
22
985
86.9
0.09
7551
0.06
-0.49
324
802
1,126
16
46
1,014
922
1,348
35
1,348
140.7
0.10
19795
0.67
-0.86
508
1,031
1,539
16
75
1,423
1,273
Estimate the dropouts for each year for FTF, FTT, and total. Paint the table using conditional
formatting.
Table 3. Estimated dropouts 2002-2016.
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
DR-F
2001
203
176
200
153
114
253
351
534
267
227
182
73
49
75
142
DR-T
DR-A
-117
86
-72
104
35
235
-370
-217
-179
-65
-48
205
-120
231
158
692
284
551
93
320
50
232
156
229
234
283
188
263
92
234
This negative dropout means some of the dropouts of previous years have come back. The
maximum dropouts were in 2009.
Prepare an excel chart incoming, graduates, dropout, and headcount over the past 16 years.
Figure 7. Incoming, graduates, dropout, and headcount, 2001-2016.
Averages: 1653, 6224, 1348, 226
7,000
6,000
5,000
4,000
3,000
2,000
1,000
0
-1,000
IN-FTA
HC-A
GR-A
DR-A
IN-FTA: all first time incoming students (FTF+FTT), HC-A: headcount of all students, GR-A: all graduates, DR-A: all
dropouts.
HC-A is inventory of College of Business and Economics that is in Little’s Law terminology, and
in our terminology, that is our headcount. Average headcount over the past sixteen years is
6224, Incoming per year, 1653, graduate average per year in the past 16 years, 1348, and
dropouts per year, 226. The title of the graph was prepared by referencing to a cell with a
formula such as ="Averages: "&D24&", "&G24&", "&J24&", "&M24.
Using the relationship between the age of data in moving average and exponential smoothing,
implement an exponential smoothing with an average data age equivalent to 6-period moving
average. Prepare a curve for all incoming, graduates, and dropouts.
The age of data in an N period moving average is simply (N+1)/2. The oldest piece of data is N
periods old; the youngest is just one year old. By some mathematical manipulations, one can
show that the age of data in exponential smoothing is 1/α. Therefore, α=2/ (N+1), and for a 6
period moving average, α=0.29.
Figure 8. Six-period equivalent moving average for incoming, graduates, dropout, and
headcount, 2001-2016.
6-period moving average equivalent
2,500
2,000
1,500
1,000
500
0
-500
IN-FTA
GR-A
DR-A
As we can see, with exception of two years, there is a gap between incoming students (FTA) and
graduating students (GR-A).
Analyze the trend in the ratio of the incoming freshmen students to incoming transfer students
(IN-FTF/IN-FTT) and the ratio of the headcount freshmen to transfer students (HC/FTF/HCFTT).
Figure 9. Ratio of the incoming freshmen students to incoming transfer students and the
headcount freshmen to transfer students.
Increase in Freshmen Population
1.1
1.0
0.9
0.8
0.7
0.6
0.5
IN-F/IN-T
HC-F/HC-T
While the ratio of incoming freshman to incoming transfer goes down over time, the headcount
of those who have come to CSUN as freshman, divided by those who have come to CSUN as
transfers, continually goes up. This understanding may help us to look at the best practices of
transfer students, and try to advertise them to our freshman students. Nevertheless, let us first
provide more evidence.
Using the Little’s Law estimate TtG for each group of students for each year. Provide 95%
confidence interval over the period of 16 years.
The Little’s Law formula is RT=I. This formula means that the throughput multiplied by the
flow time is equal to inventory. In our problem, throughput is approximated by the graduation
rate, flow time is time to graduations, and inventory is headcount. The formula can be applied
on the 16 years, and TtG for each year for FTF and FTT can be computed. Computation of
confidence interval is straight forward using an excel function
CONFIDENCE.T(0.05,N26,COUNT(N$5:N$19), where the first argument is the confidence
level, the second is the standard deviation, and the last argument is the number of observations
included in the CI.
Figure 10. 95% confidence interval for TtG of FTF and FTT.
95%CI: 7, 7.6, 8.2; 3.3, 3.5, 3.7
11
10
9
8
7
6
5
4
3
2
TtGF
TtGT
The red curve is for FTF, and the blue curve is for FTT. This time for graduation has not been
computed by going into one-by-one of students and compute the average. We have headcount
and graduates for both group of students. We can approximate TtG by using the Little’s Law.
Average TtG for FTFs 7.7, while it is 3.5 for FTT. The two numbers preceding and tailing each
average are 95%LCL and 95%UCL, respectively. The average TtG for FTT students is less than
half of the average TtG for FTFs. This is a little bit counterintuitive because, when we first
approached this problem, what we had in mind was; those who first come to CSUN are better
prepared in high school. Nevertheless, the 16—year data contradicts this perception.
All the above data & information are available on the first tab of the excel file Appendix.excel
We realize that we are doing perfect in quality-to-cost, in quality of education to tuition, but
when we transfer that space to quality-to-cost-to-time, the situation is not as good. If the
students spend two years more than it should be, then we can say the cost goes up 50%. If the
denominator goes up by 50%, the whole numerator divided by denominator will reduce to twothirds. Furthermore, if we assume that in that two years in which the students are paying
tuition at CSUN, they could have worked elsewhere, and they could have earned as much as
their tuition, then the situation at CSUN in the space of quality to cost to time would be even
worse. Finally, if we assume the student could have additional income three times per tuition,
and that is not too much because tuition is $6,000. If you have a bachelor’s degree from CSUN,
getting 3 times of it, which would be $18,000 plus itself, which is $24,000, having $24,000 per
year is not too much, and then the rectangle would have changed to this. If you go to the same
competition space, but here, we have changed the horizontal line to Quality-Time-Cost
Efficiency, then performance of all colleges, CSUN and CSU, is not good at all. The rectangle
has profoundly changed. In that situation, we could have ranked ourselves in the top three
percent of the educational institutes in the nation. This one is not so bright.
In addition, if we add a fourth dimension of variety in customer value proposition, and the
flexibility in our process competencies, then the situation gets even worse. We do not offer
enough elective courses. Core course in many hours during the day and minutes all days
during the week, and the worst situation is that we do not even offer a capacity equal to the
available demand.
Now the situation really needs to be considered, and something should be done about it. We
also use the insight gained in optimization and especially from linear programming, to
understand the binding constraints. What are the binding constraints, and which binding
constraint has the highest shadow price? We cannot mathematically implement it, but
conceptually, we need to think about it, find the binding constraints, subordinate everything to
that binding constraint, exploit the binding constraint, and try to relax it.
Let us now provide more knowledge regarding preparation of the FTF and FTT. Let us look at
their high school GPA, (HGPA), and quantitative and verbal SAT scores (SATM and SATV).
Table 4. Mean, standard deviation, and sample size of the high school GPA, Verbal SATVerbal, and SAT- Quantitative for FTF and FTT, 2001, 2016.
HGPA
SATV-F
HGPA-F
HGPA-T
SATV-F
SATM-F
SATV-T
SATM-F
SATM-T
Year
n
Xbar
s
n
Xbar
s
n
Xbar
s
n
Xbar
s
n
Xbar
s
n
Xbar
s
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
548
580
622
530
650
664
699
785
614
686
662
539
731
780
774
599
3.07
3.09
3.12
3.13
3.13
3.09
3.09
3.08
3.12
3.15
3.17
3.15
3.17
3.18
3.15
3.19
0.42
0.42
0.41
0.40
0.38
0.41
0.38
0.39
0.37
0.37
0.39
0.40
0.38
0.41
0.42
0.42
451
439
405
468
831
893
936
815
155
145
150
147
184
203
243
203
3.11
3.15
3.1
3.03
3.05
2.98
3
3.05
3.17
3.09
3.1
3.04
3.04
3.14
3.14
3.09
0.47
0.48
0.49
0.53
0.48
0.54
0.52
0.50
0.49
0.48
0.44
0.42
0.47
0.50
0.49
0.44
504
515
547
463
525
553
512
618
473
517
564
456
639
682
673
530
457.6
457
465.1
456.4
468.4
456.7
462.3
458.6
469
462.2
465.2
461.4
462.4
462
459
456.9
86.9
84.4
84.6
81.9
83.7
78.3
80.8
78.9
77.3
83.1
76.8
83.0
79.0
79.2
81.8
79.9
97
87
76
36
105
99
144
88
69
77
89
88
112
104
165
129
483.2
486
430
442.2
476.6
450.8
462.9
477.2
468.1
463.6
471.2
483.3
464.6
474.5
468.4
454.5
96.2
88.7
90.8
90.8
93.0
89.1
89.6
92.9
95.1
92.1
85.1
89.8
88.3
86.6
88.0
88.6
504
515
547
463
525
553
515
621
474
518
564
456
639
682
673
530
487.7
491.2
493.8
493.4
499.5
478.5
485.1
481
490.1
489
492.2
492.1
487.6
485.9
475.6
469.7
96.5
85.3
95.3
70.7
87.4
88.3
97.7
100.4
90.9
100.9
89.4
100.9
68.2
83.3
87.8
82.7
97
87
76
36
105
99
144
88
69
77
89
88
112
104
165
129
532.3
527.9
485.1
498.6
516.1
494.4
497.4
516.3
516.2
516.9
496.4
509.4
493.8
510.1
511
491.3
84.6
99.2
93.0
89.1
89.1
104.6
96.4
102.9
93.7
111.1
100.2
94.0
89.2
93.2
86.1
91.4
We first conduct a two tail test at 90% confidence level. The null hypothesis and alternative
hypothesis are stated as
H0: µ(HGPA-F)- µ(HGPA-T) =0
H1: µ(HGPA-F)- µ(HGPA-T)≠0
If the null hypothesis is not rejected, we can stay on it and conclude that with a 90% confidence
level, the incoming FTF and FTT show no difference. Otherwise, if the null hypothesis is
rejected by a positive test statistic, we can stay on the assumption of FTF being better than the
FTT with 95% confidence. If the null hypothesis is rejected by a negative test statistic, we can
stay on the assumption of FTT being better than the FTF with 95% confidence. The same tests of
hypotheses are stated for µ(SATV-F)- µ(SATV-T) and µ(SATV-F)- µ(SATV-T), and the same
family of conclusions are derived.
The general formula for two-tailed test of hypothesis on two samples of different sizes when
standard deviation of population is known is
Let us assume µF and µT as the means if one of the statistics associated with freshmen and
transfer students, respectively. Suppose X̅F and X̅ T are estimates of µF and µT in sample sizes
on nF and nT, respectively. Similarly, assume
and , as the standard deviations of these
statistics, and sF and sT, as their estimates in the same samples, respectively. The test statistic in
the two tail test assuming the test statistics test statistic µF - µT = d0, has a mean of
X̅F- X̅ T. For estimating the standard deviation, we used a simplified version of
𝑠2 𝑠2
√ 𝐹+ 𝑇
𝑛𝐹 𝑛 𝑇
𝑠𝐹2 𝑠𝑇2
𝑋𝐹 − 𝑋𝑇 ± 𝑡𝛼/2 √ +
𝑛𝐹 𝑛 𝑇
Were the t-variable has nF+nT-2 degrees of freedom. The excel formulas are shown below
= (C5-G5)/SQRT(D5^2/B5+H5^2/F5)
=T.INV(0.95, B5+F5-2)
=IF(ABS(B26)<=C26,0,IF(B26>0,1,-1))
Figure 11. One tail test of hypothesis on High school GPA, Verbal, and Analytical Sf AT.
H0: HGPA-F-HGPA-T>=0
1
0
-1
H0: SATV-F-SATV-T>=0
H0: SATM-F-SATM-T>=0
1
1
0
0
-1
-1
A zero value indicates none overcomes the other, +1 is for H0: being rejected with 95%
confidence level, while a-1 is for µ(HGPA-F)- µ(HGPA-T) ≤ 0 being rejected with 95% confidence
level.
Regarding the high school GPT, out of 16 experiments, in seven we were able to reject the null
hypothesis of µ(HGPA-T)≥ µ(HGPA-F), and in one experiment we rejected the null hypothesis of
µ(HGPA-F)≥ µ(HGPA-T). A ratio of 7/1 in the benefit of FTFs.
Regarding the high verbal SAT, out of 16 experiments, in one experiment we were able to reject
the null hypothesis of µ(SATV-T)≥ µ(SATV-F), and in four we rejected the null hypothesis of
µ(SATV-F)≥ µ(SATV-T). A ratio of 4/1 in the benefit of FTTs.
The situation in quantitative SAT got even better for transfer students. No experiment
supported the null hypothesis of µ(SATM-T)≥ µ(SATM-F), while the null hypothesis of
µ(SATM-F)≥ µ(SATM-T) was rejected nine times. It seems we can stay on the null hypothesis of
the transfer students having a better SAT performance. According to Brint 2017, about twothirds of the variance in six-year graduation rates in the United States can be explained by the
average SAT/ACT score of entering freshmen.
All the above data & information are available on the second tab of the excel file Appendix.excel
Now let us see if the FTFs understand their limitations in workload they select in each semester.
The
Table 5. Full Time Equivalent (FTE) of incoming FTF and FTT (columns 2 and 3), and FTE of
all the student population who have entered as FTF and FTT, respectively (columns 4 and 5).
Year
IN-FTF
IN-FTT
HC-F
HC-T
HC-F less IN-FTF
HC-T less IN-FTT
2001
491.3
643.6
1,899.1
2,481.7
1,407.8
1,838.1
2002
515.5
564.5
1,998.5
2,460.9
1,483.0
1,896.4
2003
562.4
539.5
2,117.2
2,351.5
1,554.8
1,812.0
2004
471.3
510.4
2,110.7
2,144.1
1,639.4
1,633.7
2005
582.5
740.8
2,306.3
2,503.1
1,723.8
1,762.3
2006
612.9
746.2
2,478.1
2,587.7
1,865.2
1,841.5
2007
636.7
770.5
2,513.7
2,669.2
1,877.0
1,898.7
2008
691.8
690.7
2,538.9
2,658.5
1,847.1
1,967.8
2009
545.3
661.3
2,237.3
2,466.9
1,692.0
1,805.6
2010
617.9
781.6
2,248.1
2,307.0
1,630.2
1,525.4
2011
611.2
825.2
2,350.7
2,365.9
1,739.5
1,540.7
2012
496.8
641.9
2,324.1
2,284.1
1,827.3
1,642.2
2013
668.5
897.9
2,570.6
2,272.4
1,902.1
1,374.5
2014
700.7
952.8
2,833.9
2,362.1
2,133.2
1,409.3
2015
707.7
961.7
2,980.5
2,600.2
2,272.8
1,638.5
2016
543.7
791.2
2,933.8
2,575.6
2,390.1
1,784.4
Column 6 is simply column 4 minus column 2, and column 7 is column 5 minus column 3. By
dividing these FTE numbers by their corresponding headcounts, Figure XXX is obtained.
Figure 12. Per capita FTE for incoming FTF and FTT, and the total FTF and FTT student
population net of current incomings.
Averages: 0.89, 0.74, 0.83, 0.72
95.0%
90.0%
85.0%
80.0%
75.0%
70.0%
65.0%
In-F
In-T
Inv-Net-F
Inv-Net-T
As we can observe, our brave FTF students, against their capabilities, continually carry more
load compare to FTTs. Over the period of 16 years, FTF in their first year had a load 0.89/0.74=
1.2 times of the incoming FTT. The overall FTF population, net of the current hear incoming had
a load of 0.83/0.72 = 1.15 times the overall FTT population, net of the current hear incomings.
One of the best practices that can be bench marked is to encourage the FTF to take a smaller
number of courses, both in the first semesters, as well as throughout their education.
Table 6.
FTF Headcount
2007
2008
2009
717
815
646
Year
1
2001
576
2002
596
2003
626
2004
543
2005
663
2006
688
2010
709
2011
715
2012
592
2013
780
2014
826
2015
817
2016
628
2
401
422
473
515
429
578
538
513
3
385
435
470
483
489
458
552
498
4
328
380
421
447
479
488
427
5
308
276
291
338
363
398
6
163
195
147
151
184
7
53
80
86
66
8
30
35
37
9
19
22
10
17
11+
Total
Mean
%
684
23.8%
568
483
555
558
493
677
715
716
540
18.8%
448
525
442
558
594
540
725
707
519
18.1%
500
408
416
487
429
540
561
530
686
470
16.4%
380
322
325
297
293
344
318
441
400
382
342
11.9%
189
211
190
139
143
114
117
138
126
174
165
159
5.5%
78
83
93
94
68
56
47
44
46
61
56
67
67
2.3%
41
29
37
33
48
35
31
22
25
18
26
30
24
31
1.1%
21
24
21
11
27
14
26
15
19
10
8
8
14
18
17
0.6%
8
15
9
11
14
11
15
11
20
6
14
8
7
5
9
11
0.4%
49
40
35
26
26
25
32
30
30
29
33
20
22
23
19
26
29
1.0%
2,329
2,489
2,622
2,643
2,772
2,969
3,021
3,039
2,704
2,724
2,733
2,711
2,965
3,296
3,485
3,428
2,871
1
=IFERROR(INDEX($C$5:$R$15,ROWS($C$5:C5),ROWS($C$5:C5)+COLUMNS($C$5:C5)-1),"")
Table 7.
Year
1
2001
576
2002
596
2003
626
2004
543
2005
663
2006
688
2007
717
2008
815
2009
646
2010
709
2011
715
2012
592
2013
780
2014
826
2015
817
2
422
473
515
429
578
538
513
568
483
555
558
493
677
715
716
3
470
483
489
458
552
498
448
525
442
558
594
540
725
707
4
447
479
488
427
500
408
416
487
429
540
561
530
686
5
363
398
380
322
325
297
293
344
318
441
400
382
6
189
211
190
139
143
114
117
138
126
174
165
7
93
94
68
56
47
44
46
61
56
67
8
48
35
31
22
25
18
26
30
24
9
26
15
19
10
8
8
14
18
9
10
20
6
14
8
7
5
11+
33
20
22
23
19
26
`
1
2
3
4
5
6
7
8
9
10
11+
2001
100%
73%
82%
78%
63%
33%
16%
8%
5%
3%
6%
2002
100%
79%
81%
80%
67%
35%
16%
6%
3%
1%
3%
2003
100%
82%
78%
78%
61%
30%
11%
5%
3%
2%
4%
2004
100%
79%
84%
79%
59%
26%
10%
4%
2%
1%
4%
2005
100%
87%
83%
75%
49%
22%
7%
4%
1%
1%
3%
2006
100%
78%
72%
59%
43%
17%
6%
3%
1%
1%
4%
2007
100%
72%
62%
58%
41%
16%
6%
4%
2%
1%
2008
100%
70%
64%
60%
42%
17%
7%
4%
2%
2009
100%
75%
68%
66%
49%
20%
9%
4%
2010
100%
78%
79%
76%
62%
25%
9%
2011
100%
78%
83%
78%
56%
23%
2012
100%
83%
91%
90%
65%
2013
100%
87%
93%
88%
2014
100%
87%
86%
2015
100%
88%
2016
628
2016
100%
Figure 13.
100%
2001
2002
2003
2004
2005
80%
2006
2007
2008
2009
2010
60%
2011
2012
2013
2014
2015
40%
20%
0%
1
24:20
2
3
4
5
6
7
8
9
10
11
16-Years Retention and Graduatiholon Rates: Class 2001
I have looked at 16 years of data, here is 2001; in 2001, this is the population in [College
of Business and Economics] for the first year, for the second year, and this is the number of
students that have been in the College of Business in the year 2001, for 10 years. Now, if I go to
2002, and look at those people who have been in CSUN for two years, then I get these numbers.
Moreover, of course, these 422 are those 576, and the rest have dropped out. Therefore, if I
continue on the diagram, this is the population of 2001 College of Business entering students
through an 11-year period. I can do the same for 2002, move on the diagonal, see what has
happened to them, and 2003, and so forth. Then I can create this table.
25:40
16-Years Retention and Graduation Rates: Class 2001
&
16-Years Retention and Graduation Rates: 2001-15
So this is what has happened to 2001 students, and if you see that at the 11th point the
curve a little bit goes up, it is because after 11 years, some of [the dropouts] have come back.
This is 2002, 2003, 2004, 5, 6… and this is all the 16 years. I have the average over there, these are
the maximums, and these are the minimums. Obviously, in the first four years, you want this
curve as flat as possible. After that, we like to have a sharp slope. This is the same thing with
95% confidence interval, so these are the maximums, these are the minimums, here we like the
maximums, and here we like the minimums.
26:45
16-Years Retention and Graduation Rates: UCL95%CI, LCL95%CL, Exponential Smoothing [g=0.29]
These are 2015 entering students, freshman students, so they are about average. It is
good. Moreover, these are 2014, these are 2013 first-time freshman at College of Business and
Economics, and all of them are about average, so things are getting relatively better here.
27:09
Required Number of FTF Graduates
Here is the number of graduates we need to follow a specific time to graduation. The black dots
we see are our position in the past 16 years. The blue line is the required number of graduates to
need an average of seven-year time to graduation. As we see in 2016, we are around there, a
little bit even better. In some years in the past 16 years, we were below average of seven-year
time to graduation, in some years we were above. If you are looking at five-year average time to
graduation, then the current headcount of College of Business and Economics, we need about
700 graduates per year.
28:11
Required % Increase in # of Graduates
These are the same numbers, but we have translated them into percentage increase in
compared to our current position. In addition, this is 6-year moving average of these numbers,
or, an exponential smoothing of about 0.3 Therefore in the current position in 2016, this is our
current situation, which is more or less about a seven years average time to graduation. We
need about 20% increase if we want to go for six years’ time to graduation, about 45 to 50%
increase if you want to go for an average of five years’ time to graduation, and about 75%
increase in our current number of graduates if you want to go for four years’ time to
graduation. About 75% increase in this number.
29:24
160,000 Records for 16-Years Performance
This is about 160,000 records in the past 16 years. I have collected about 10,000 records
per year. I have partitioned our lower division courses and core courses into three groups; those
with high taste of quantitative, those with high qualitative taste, and those in between.
Therefore, here are before Gateway classes. I have defined Gateway as a milestone, to check
what has happened and foresee what will happen, but in each of these periods, we implement
qualitative tools to see what we think we will be in the future. This will be applied to groups of
students. We can look it at the very macro-level, or we can go down and look at it at the very
micro-level.
30:44
Information-Analytics
We try to implement descriptive analytics. Descriptive analytics is to understand what
has happened in the past 16 years, and that is mainly to transfer data into information. Then we
try to do diagnostic analytics to find the root and effect analysis. Why it happened, and that is
indeed transformation of information into knowledge. Then we conduct predictive analytics,
and we try to foresee what is likely to happen, and that is mainly transformation of knowledge
into understanding. Finally, we try to develop Prescriptive Analytics models, and to learn what
we should do about it, and it is mainly, hopefully, transformation of understanding into
wisdom.
32.04
Big Data
We try to use tools such as Excel, Tableau, Tableau is not an analytical tool, Tableau is a
visual tool, presentation tool, but we also use Jmp, which is more of an analytical tool, and also,
we will use Frontline Solvers in this process.
32:30
Systems Thinking; Rumi-Elephant in the Dark
Therefore, we talked about one of our teachers, John Little, and we used the process flow
concept to understand the flow. We talked about another teacher, George B. Dantzig , which,
using his concepts in linear programming, we will try to find out which binding constraints
have the highest shadow prices, and try to understand them exploit. Now we talk about our
other teacher who tries to tell us to have a system here.
21:45
Systems Thinking [VIDEO]
“In the nineteen fifties, the Dayak people of Borneo, an island in Southeast Asia,
were suffering from an outbreak of Malaria, so they called the World Health
Organization for help. The World Health Organization had a ready-made solution, which
was to spray copious amounts of DDT around the island. With the application of DDT,
the mosquitos that carried the Malaria were knocked down and so was the Malaria. There
were some interesting side effects though. The first was that the roofs of people’s houses
began to collapse on their heads. It turns out the DDT not only killed off the Malaria
carrying mosquitos, but also killed a species of parasitic wasps that had controlled a
population of thatch-eating caterpillars. Thatch being what the roofs at the Dayak
people’s homes were made from. Without the wasps, the caterpillars multiplied,
flourished, and began munching their way through the villagers’ roofs. That was just the
beginning. The DDT affected a lot of the island’s other insects, which were eaten by the
resident population of small lizards called geckos. The biological half-life of DDT is
around eight years, so animals like geckos do not metabolize it very fast. It stays in their
system for a long time. Over time, the geckos began to accumulate high levels of DDT. In
addition, while they tolerated the DDT fairly well the island’s resident cats, which dined
on the geckos, did not. The cats ate the geckos, and the DDT contained in the geckos
killed the cats. With the cats gone, the islands population of rats came out to play. We all
know what happens when rats multiply and flourish. Soon the Dayak people were back
on the phone with the World Health Organization, only this time it was not Malaria that
was the problem, it was the plague, and the destruction of their grain stores, both of
which were caused by the overpopulation of rats. This time though, the World Health
Organization did not have a ready-made solution, and had to invent one. What did they
do? They decided to parachute live cats into Borneo. Operation Cat Drop occurred
courtesy of the Royal Air Force and eventually stabilized the situation.” “If you don’t
understand the inter-relatedness of things, solutions often cause more problems.”
Rumi – An Elephant in the Dark
Some Hindus were exhibiting an elephant in a dark room, and many people
collected to see it. However, as the place was too dark to permit them to see the elephant,
they all felt it with their hands, to gain an idea of what it was like. One felt its trunk, and
declared that the beast resembled a water pipe. Another felt its ear, and said it must be a
large fan. Another it is leg, and thought it must be a pillar. Another felt its back, and
declared the beast must be like a great throne. According to the part which each felt, he
gave a different description of the animal?
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