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Undergraduate Statistics Curriculum: A Large,Unstructured, Complex ProblemConnie M. Borror a , Roger L. Berger a , Sue LaFond a & Melanie Stull aa New College Interdisciplinary Arts and Sciences , Arizona State University at the WestCampus , Phoenix , ArizonaPublished online: 26 Mar 2012.

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Undergraduate Statistics Curriculum: ALarge, Unstructured, Complex Problem

Connie M. Borror,

Roger L. Berger,

Sue LaFond,

Melanie Stull

New College Interdisciplinary

Arts and Sciences, Arizona State

University at the West Campus,

Phoenix, Arizona

ABSTRACT In this article, we present an approach used to develop an

undergraduate statistics curriculum. With the continually evolving work-

place, graduates with statistics degrees are being called upon to fill many

new and diverse roles in every type of enterprise. As a result, the undergrad-

uate statistics curriculum must also evolve and equip new graduates with

tools, methods, and problem-solving skills to meet new challenges in busi-

ness, industry, nonprofit organizations, and government agencies. In our

approach, we viewed curriculum development and implementation as a

large, unstructured, and complex problem, the type of problem that is well

suited to the use of statistical engineering for its solution. The development

of this 4-year degree program is a work in progress, but an integral part of

the program includes courses and opportunities for students to develop

statistical engineering skills. Examples and recommendations are provided.

KEYWORDS statistical engineering, use-inspired curriculum

INTRODUCTION

Hoerl and Snee (2010) defined statistical engineering (SE) as ‘‘the study of

how to best utilize statistical concepts, methods, and tools and integrate

them with information technology and other relevant sciences to generate

improved results’’ (p. 12). The authors further identified five phases that

could constitute the ‘‘building blocks’’ of statistical engineering projects:

1. Identify problems: find the high-impact issues inhibiting achievement of

the organization’s strategic goals.

2. Create structure: carefully define the problem, objectives, constraints,

metrics for success, etc.

3. Understand the context: identify important stakeholders (customers,

organizations, individuals, management), research the history of the

issue, identify unstated complications and cultural issues, and locate rel-

evant data sources.

4. Develop a strategy: create an overall, high-level approach to attacking

the problem, based on Phases 2 and 3.

5. Establish tactics: develop and implement diverse initiatives or projects

that collectively will accomplish the strategy.

Address correspondence to Connie M.Borror, New College InterdisciplinaryArts and Sciences, P.O. Box 37100,Arizona State University at the WestCampus, Phoenix, AZ 85069-7100,USA. E-mail: conni@asu.edu

Quality Engineering, 24:201–214, 2012Copyright # Taylor & Francis Group, LLCISSN: 0898-2112 print=1532-4222 onlineDOI: 10.1080/08982112.2011.652005

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The Hoerl and Snee (2010) SE definition com-

bined with the five-phased approach outlined above

were used to develop an undergraduate statistics cur-

riculum at the West Campus of Arizona State Univer-

sity (ASU). Although not referred to as ‘‘Phase 1,

Phase 2, . . . ’’ in the proposal to the Arizona Board

of Regents, the process used is well-defined using

the five phases outlined by Hoerl and Snee (2010).

In the next section, we briefly describe the culture

within the state of Arizona, ASU, and the West Cam-

pus of ASU that underscored the need for a bache-

lor’s degree in statistics. Following that discussion,

we describe how the five-phased approach applies

to curriculum development. In subsequent sections,

we describe important components of individual

courses necessary to provide a framework for the

undergraduate statistics program which will prepare

majors for careers as innovators in any enterprise.

We have borrowed liberally from many different

fields as well as from discussions on undergraduate

statistics curricula such as Moore (2001) and Bryce

et al. (2001). We have created this curriculum with

the goal of providing students with the necessary

tools to be successful beyond the classroom. In our

view, a successful student is one who has obtained

the skills, creativity, and confidence to approach

and solve complex problems as well as discover

new ideas; and when they do, they have enough

solid background to recall information and then

develop more knowledge in an area. That is our idea

of a ‘‘successful’’ statistics major.

BACKGROUND

Within the Division of Mathematical and Natural

Sciences on the West campus of ASU, there are four

core programs, each with its own 4-year bachelor of

science (B.S.) degree: Applied computing, applied

mathematics, life sciences, and statistics, with the

B.S. in statistics having been approved in 2010. All

four core areas are separate from programs offered

on any of the other three ASU campuses.

Because the Division of Mathematical and Natural

Sciences has such great depth and breadth, we have

many opportunities for collaboration through

research and teaching with our emphasis being

undergraduate education. Bringing together expert-

ise in all of these areas allows our students to experi-

ence many different applications of topics in

statistics, computing, biology, chemistry, forensic

science, and mathematics. Students majoring in stat-

istics on the West campus can take classes in these

disciplines or in other disciplines offered in the

New College of Interdisciplinary Arts and Sciences

on the West campus, or they can take classes in the

other colleges and schools located on one or more

of the four campuses of ASU. According to some

measures, ASU is the largest university (by enroll-

ment) in the United States. This provides rich oppor-

tunities for a potential statistics major. But, until 2010

ASU did not offer a statistics degree, nor did any

other university in the state of Arizona. This is the

‘‘blank slate’’ upon which we developed the new

B.S. in statistics.

It is the goal of the New American University

approach at ASU to provide an opportunity to attend

a postsecondary educational institution for a large

majority of students that may not exist at other institu-

tions. Undergraduate admission requirements for

freshmen at ASU require a high school diploma, com-

pletion of ASU competency requirements with a 2.0

grade point average (GPA) for individual courses,

and fulfillment of one of the following criteria: high

school standing in the top 25% upon graduation, mini-

mum cumulative GPA of 3.0 on a 4.0 scale in the ASU

competency courses, and a minimum ACT (formerly

known as American College Testing) score of 22 or a

Scholastic Aptitude Test (SAT) Reasoning score of

1040 for Arizona residents. For nonresidents an ACT

score of 24 or SAT Reasoning score of 1110 is

required. In addition, accepted freshmen may be

admitted to ASU with up to two deficiencies in the

ASU competency areas as long as the deficiencies do

not occur in mathematics and a laboratory science.

Furthermore, many of the students who attend ASU’s

New College of Interdisciplinary Arts and Sciences

are the first in their families to attend a postsecondary

4-year institution.

Retention of this very different student will focus

on student support and student engagement on mul-

tiple levels. Of primary importance with regard to

student retention is interaction with the faculty. As

stated by Cuseo (2007), student–faculty interaction

fosters an atmosphere that enhances critical thinking

skills, promotes academic achievement, and retains

students in the program. The proposed structure of

the statistics major reflects this atmosphere and will

allow faculty mentoring opportunities to evolve as

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students progress through the degree program. In

addition, the college employs a dedicated pro-

fessional academic advising staff to monitor student

progress toward graduation. Students meet with their

advisor multiple times throughout their academic

career to discuss status, progress, and strategies for

success.

INTEGRATING STATISTICALENGINEERING AND A STATISTICS

CURRICULUM

In this section, we present our approach to devel-

oping an undergraduate statistics curriculum within

an interdisciplinary arts and sciences college to pro-

vide students with a holistic approach to statistical

thinking.

Phase 1: Identify Problems

Demand for continuous improvement and cost

reduction in business, industry, and government

(for example, Six Sigma and Lean initiatives) will

require more in-depth statistical skills than are cur-

rently offered by any undergraduate program in the

state of Arizona. Arizona is the 16th largest state in

terms of population and the only state in the top

20 without at least one university offering a bache-

lor’s degree in statistics. A bachelor’s degree in stat-

istics would support the university’s goals of

providing an interdisciplinary education that will

involve community engagement and service. In

addition, the proposed statistics curriculum supports

the university’s learning outcomes of developing

mathematical skills, success in application of techni-

cal knowledge, and skill in the gathering and utiliza-

tion of information to enhance knowledge and

advance innovation.

Phase 2: Create Structure

Twenty years ago, undergraduate degrees in stat-

istics were rare but, according to the American Stat-

istical Association, now over 70 universities offer

such degrees. The growth in programs is due to

the increasing demand for statisticians and to the fact

that now students are learning about statistics in high

school, mainly through advanced placement (AP)

statistics courses (context). The AP statistics exam

was first administered in 1997 to about 7,600 stu-

dents, and the number of students taking the exam

has grown by about 10% each year. In 2006, 2007,

2008, and 2009, the number of students taking the

AP statistics exam was 88,237, 98,033, 108,284, and

116,876, respectively. As a result, many high school

graduates now have familiarity with statistics and

seek a degree in statistics. Currently there are no

undergraduate degrees in statistics offered in the

state of Arizona to meet the increasing demand from

incoming students, business, industry, and govern-

ment (problem). Some programs offer mathematics

degrees with a focus or concentration in statistics

but with far less depth of education in statistics than

the proposed degree and most without a more holis-

tic approach to statistics education as proposed here.

The objectives of the proposed curriculum are to

prepare undergraduate students with the statistical

tools, methods, and problem-solving skills to be

innovative and adaptive to an ever-changing work-

force and make a considerable difference with high

impact for any enterprise. The objectives can be ful-

filled through:

1. Strong statistical and nonstatistical content—

through varied statistics courses that require not

only how to use statistical methods and

problem-solving skills but also nonstatistical skills

such as technical writing, oral presentations, man-

agement skills, team dynamics, and finance as it

relates to statistics. Within these environments

(courses), students must learn to work both inde-

pendently and as a member of a team while mas-

tering the content.

2. An area of focus—a collection of courses in a spe-

cific discipline of interest to the student. The focus

area provides a portion of the ‘‘other relevant

sciences’’ in Hoerl and Snee’s definition of statisti-

cal engineering. An area of focus further supports

the interdisciplinary education goals of the

university.

3. A senior capstone course—a required course

where students work on a problem whose sol-

ution will provide high-impact results for a busi-

ness, industry, nonprofit, or government agency

through the use of both statistical and nonstatisti-

cal skills and methods. Students will work in

teams of three to four on a problem that is of vital

importance to an enterprise. This course will not

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be successful without partnerships with business

and industry (or nonprofits=governmental agen-

cies). These external sponsors will supply the

problem to be solved and provide a contact

(i.e., a champion within the company) with

whom the students can meet on a biweekly basis

or more often during the semester.

Metrics to be measured will include the following:

. student retention and graduation rates;

. successful employment placement and retention;

. pursuit of graduate work;

. national and international reputation of the stat-

istics program; and

. long-term relationships with business, industry,

nonprofit, and governmental organizations (i.e.,

enterprises that work with the division to provide

real-world problems whose solutions are

developed by the student teams in the senior cap-

stone course.)

Our goal is to demonstrate to companies that our stu-

dents can think critically and solve complex prob-

lems and that working with our students provides a

significant return on their investment (investment

of time, and in future monetary savings). In turn,

companies will continue to provide problems

(opportunities) every semester for our students.

Phase 3: Understand the Context

The important stakeholders include the students,

the university, business, industry, nonprofit and

government agencies, and society in general. Being

able to produce graduates who are successful inno-

vators and problem solvers is of importance to every-

one. Developing a curriculum that can produce

educated citizens has to include important compo-

nents. We gathered data from various sources to

determine best practices and identify core competen-

cies that should be part of an undergraduate statistics

curriculum. We drew not only from undergraduate

statistics programs around the world but also from

engineering departments, business schools, business

and industry, and professional societies for ideas and

recommendations concerning key attributes a gradu-

ate would need to be successful in the workforce or

graduate studies. For example, two themes weaved

into the entire curriculum—how we use real-world

problems and technical writing—were modeled after

two programs: (1) the senior engineering project

course in the Department of Industrial and Enter-

prise Systems Engineering (ISE) at the University of

Illinois at Urbana–Champaign (UIUC); and (2) the

Department of Mathematics at Harvey Mudd College.

They represent some of the best practices for parti-

cular core competencies that we want our statistics

students to master.

Our goal was to put in place a process involving

best practices that would provide a framework for

new course development and implementation, a

structure that is not people driven (i.e., the entire

major is dependent on what faculty you have or no

longer have) but process driven while still encour-

aging faculty independence. We attended meetings

of and researched literature from a wide range of

professional societies, including the American Stat-

istical Association, the American Society for Quality,

the American Society for Engineering Education,

the Institute for Operations Research and Manage-

ment Science, the Decision Sciences Institute, the

Society for Manufacturing Engineers, and the Royal

Statistical Society, to name a few.

Within ASU, we met with other divisions and dis-

ciplines to identify areas of focus and experts in non-

statistical areas. The focus area is integral to

providing a diverse and well-rounded experience

for the student. By identifying faculty with expertise

in nonstatistical arenas such as team dynamics, lead-

ership, psychology, and project management; for

example, we can collaborate with faculty by offering

seminars and workshops for students.

There are of course a number of potential barriers

to successful implementation of curriculum. Three of

the more potentially problematic would be the

following:

1. Lack of participation by business=industry=acade-

mia. The success of the proposed program

depends heavily on participation by business,

industry, academia, or other enterprises providing

real-world problems for the upper-level statistics

courses. Even if a real problem is provided, it

must be of vital importance to the enterprise or

sponsoring organization. If it is not, then support

by the sponsoring organization can fade over a

very short period of time and students end up

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losing access to important enterprise information

needed to complete the project. In these

instances, students begin to have diminishing

access to their sponsor contact because focus

has shifted within the organization and the once

important problem is no longer of interest.

2. Weak solutions to industry problems. Student

solutions to industry sponsors’ problems must

be viable and meaningful. If students provide

weak, irrelevant, or unrealistic solutions, sponsors

are unlikely to support the statistics program with

future projects. Weak solutions can be minimized

by emphasizing problem-solving skills through-

out the statistics curriculum and active partici-

pation by the industry sponsor.

3. Lack of support within the university. A third key

component to the success of the program is sup-

port by administration to foster collaboration

among divisions and colleges within ASU. With-

out this support, it will become more difficult

for students to enroll in courses in disciplines

outside their major. It is absolutely necessary that

students be allowed to enroll in courses in their

area of focus, which we encourage to be outside

their major. Some disciplines do not allow

non-majors to enroll in their courses or new

permission must be sought for every student

for every class they wish to take; seeking per-

mission on a case-by-case basis is a non-value-

added task and will add to the unnecessary

complexity of the enrollment process. An agree-

ment with different disciplines at the onset would

result in more streamlined enrollment and foster

better collaboration.

A second concern within the university is the

ever-growing practice of differential tuition. Some

disciplines within the university are beginning to

charge students more in terms of fees and tuition

to become majors. In addition, tuition is differen-

tiated by campus within ASU. For example, begin-

ning in the 2011–2012 academic year, tuition for an

undergraduate student at the West Campus and Poly-

technic campus of ASU was 10% less than the tuition

at the Downtown and Tempe Campuses of ASU. A

concern is whether differential tuition by discipline

or campus within ASU will deter students from

choosing an area of focus in that discipline because

of cost or inability to enroll in a course. We hope

to alleviate this problem by establishing and main-

taining an open dialogue with other departments

and campuses about our students enrolling in

non-major courses.

Phase 4: Develop a Strategy

The goals of the statistics program are as follows:

. To enable graduates to identify and quantify vari-

ation.

. To enable graduates to use their statistical and

nonstatistical skills to solve real-world problems.

. To enable graduates to engage in lifelong learning

and self-education.

The strategies in place to reach these goals are as

follows:

1. Offer a use-inspired curriculum.

2. Emphasize the identification and understanding

of variation.

3. Emphasize nonstatistical skills.

4. Maintain a high-level community-embedded pro-

gram.

Strategies 2 and 3 are straightforward with tactics for

these strategies discussed in the following sections.

Strategies 1 and 4 are outcomes of one of ASU’s goals

of conducting ‘‘use-inspired research’’ (Crow 2010).

Use-inspired research is an integration of research

for theoretical purposes and research motivated by

real-world problems (Stokes 1997). We feel that a

curriculum should be based on the same principles,

providing sound theory while demonstrating need

using real problems and applications.

Phase 5: Establish the Tactics

Tactics supporting the strategies and achieving

overall goals of the undergraduate statistics program

are listed in Table 1. The tactics listed are student

centered and involve students developing

problem-solving skills and using these skills for

many different types of problems.

More details on the strategies and tactics are pro-

vided in the following sections. The recommenda-

tions in these sections are not new, and many

statistics programs use most of these tactics. Just as

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Six Sigma involved a methodology composed of

tools that were not new, the program we propose

is a composition of best practices used in a variety

of fields including, but not limited to, statistics, busi-

ness, psychology, engineering, and mathematics.

COMPONENTS OF ANUNDERGRADUATE STATISTICS

CURRICULUM

A statistical engineering–based curriculum is what

we are proposing. The components of such a cur-

riculum are varied but necessary to prepare new

graduates in statistics who will face challenges in

the workforce not seen in previous generations.

We envision an SE-based curriculum that includes

theory, methods, data management, team building,

problem solving, and communication skills. It will

include structure for students to learn how to solve

problems using a combination of statistical methods

and nonstatistical skills. In this section, we discuss

one approach to integrating statistical engineering

into an undergraduate curriculum.

Core Competencies

An SE-based curriculum must include some spe-

cific core competencies. The proposed (and now

approved) curriculum is outlined in Table 2. The

required courses, elective statistics courses, and

required mathematics and computing courses are

fairly typical for an undergraduate applied statistics

degree. An area of focus will consist of nine or more

semester hours of coursework in the student’s cho-

sen field of interest. The faculty and staff can assist

students in identifying courses in an area of their

interest. Some example focus areas are displayed in

Table 3. What can make this curriculum different

TABLE 2 Statistics, mathematics, and computing courses required and elective for the B.S. in statistics

Required statistics courses

Required mathematics and

computing courses Statistics electives (choose two)

Calculus-based Probability and

Statistics I, II (6 hours)

Calculus w=Analytic

Geometry I, II, III (12 hours)

Quality Improvement and Reliability (3 hours)

Applied Regression Analysis=Time

Series (3 hours)

Applied Linear Algebra (3

hours)

Categorical Data Analysis (3 hours)

Design and Analysis of

Experiments (3 hours)

Introduction to Computer

Science (3 hours)

Nonparametric Analysis (3 hours)

Statistical Computing (3 hours) Multivariate Analysis (3 hours)

Mathematical Statistics (3 hours) Stochastic Processes (3 hours)

Senior Capstone Project (3 hours)

TABLE 1 Strategies and tactics for reaching program goals

Strategies Tactics

Offer a

use-inspired

curriculum

External sponsor projects

Student-initiated projects

Faculty-defined projects

Exploration courses

Peer mentoring

Senior capstone experience

External enterprise surveys and

feedback

Institute a program advisory

board

Emphasize the

identification

and

understanding

of variation

Problem-based learning

Cooperative learning

Homework

Projects

Quizzes

Exams

Emphasize

nonstatistical

skills

Problem-based learning

Cooperative learning

Teamwork and leadership projects

Oral presentations

White papers

Written technical reports

Homework

Quizzes

Exams

Maintain a

high-level

community-

embedded

program

Exit surveys (upon graduation)

Alumni evaluations (1-, 3-, 5-,

10-year)

Employer surveys

Sponsoring organization surveys

Institute a program advisory

board

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from the standard statistics curriculum is in the deliv-

ery of material, the types of open-ended problems

students are asked to solve, and nonstatistical

requirements.

The core competencies of the new degree include

but are not limited to statistical methods and theory.

For a more holistic approach to undergraduate stat-

istics education, we are employing a three-level

tiered model displayed in Figure 1. We envision

the components of each level as hierarchical and par-

allel. Students will utilize each level of the paradigm

in Figure 1 at all stages of their undergraduate edu-

cation (parallel), but they need a solid foundation

to build on (hierarchical). As we see it, competencies

at Levels 2 and 3 provide the framework that will

move students from being users of statistical tools

and methods to innovators and users of statistical

thinking. Level 3 components should be integrated

into all academic levels, including first-year courses.

Course goals should focus on these components

through two key aspects of statistical engineering:

(1) active learning and (2) developing viable solu-

tions to real-world (often complex) problems. Level

1 provides the foundation, a foundation that they will

revisit in each course in the curriculum, and a foun-

dation that if it is not rigorous enough, the student’s

success in the program will be much less.

We place significant emphasize on writing techni-

cal reports and presenting results to a wide audience.

These issues cannot be overemphasized. One good

benchmark for introducing technical writing to the

first-year or second-year student is the Department

of Mathematics at Harvey Mudd College. An early

introduction to word processing and document

preparation tools (e.g., LaTex) is an important aspect

of students’ understanding and reporting of results in

a clear professional manner. Being able to convey

technical ideas and solutions to a general audience

is an SE skill that is essential for a statistician in

today’s economy. Technical writing and oral presen-

tations should be emphasized at varying degrees in

all statistics courses.

FIGURE 1 Core competencies of a B.S. degree in statistics at

the West Campus of Arizona State University. (Color figure

available online.)

TABLE 3 Sample areas of focus with courses for statistics majors

Chemistry

Computer

Science Mathematics

Engineering

Management Finance Sustainability DNA science�

General

Chemistry I

Principles of

Computer

Science

Discrete

Mathematical

Structures

Introduction to

Engineering

Design

Uses of

Accounting

Information

Design for

Ecology and

Social

Equity

Biology I

General

Chemistry II

Data Structures

and

Algorithms

Advanced

Calculus I

Work Analysis

and Design

Managerial

Accounting

Industrial

Design

Biology II

General Organic

Chemistry I

Introduction to

Database

Systems

Applied

Computational

Methods or

Mathematical

Models in

Biology

Engineering

Administration

Macro

Economics

Global Impact

Entrepre-

neurship

Fundamentals of

Genetics

General Organic

Chemistry II

Discrete

Mathematical

Structures

�Would require Gen. Chemistry I and Gen. Chemistry II to complete.

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Finally, it is worth noting that the single most

important core competency would be understanding

variability. Students must understand that statistics

as a field of study exists because variability exists

everywhere—manufacturing, service industries,

health care, etc. As obvious as it may seem to those

of us who have studied variability in different con-

texts, the concept of variability and how to measure

it is not always obvious to students (see

Meletiou-Mavrotheris and Lee 2002; Reading and

Shaughnessy 2004). Providing students with prob-

lems and opportunities to discover the role of vari-

ation in all types of processes will reinforce the

concept. Hjalmarson et al. (2011) described an exer-

cise used to evaluate and improve the understanding

of variation by first-year undergraduate engineering

students.

Peer Mentoring and ExplorationCourses

Within the Division of Mathematical and Natural

Science (MNS), the Bachelor of Science degree in life

sciences offers the opportunity for undergraduate

students to earn academic credit by mentoring their

peers in the laboratory classroom. The peer mentor

must have previously completed the course success-

fully and can only enroll in the course with per-

mission of the instructor of record. The role of the

peer mentor is to assist the lab instructor with basic

laboratory procedures and to provide guidance to

the students as they complete the lab protocol. This

position is highly sought after by upper-level under-

graduates in the program and it affords them experi-

ence that would not normally be available to an

undergraduate student. Peer mentoring builds cama-

raderie between students and reinforces a sense of

community within the program. Likewise, such an

opportunity would be beneficial for the incoming

statistics majors. Upper-level undergraduates would

have the opportunity to share their knowledge and

problem solving skills with incoming freshmen. In

turn, freshmen will benefit from the experience by

connecting with successful students in the program.

The bachelor of science life science major also

offers a course that exposes students to a variety of

career opportunities for student pursuing this major:

‘‘careers in the natural and health sciences.’’ The

course focuses on how to obtain experience in the

student’s chosen field as well as hosting a variety

of professionals from the community to present in

a seminar format. A similar course is planned for

the statistics major. The development of this course

will include building interpersonal skills and connec-

tions, ‘‘statistics as a profession’’ and will also intro-

duce students to various professionals from the

community as guest speakers. Workshops will

emphasize team work, communication, and techni-

cal writing skills. Inviting professionals in the com-

munity to share their knowledge in the classroom

setting serves two purposes. Students are exposed

to local experts in a variety of disciplines, promoting

networking opportunities as well as introducing

career pathways students may not have previous

considered. By integrating students within the stat-

istics major with professionals early in the program,

opportunities are created for student to apply their

problem-solving skills to local issues that may impact

their own communities. Social embeddedness is one

of the eight design aspirations of the New American

University at ASU.

The exploration course is a one credit-hour self-

directed course that can be repeated for a total of 2

credit hours. The course is designed for first- or

second-year statistics majors to explore various fields

of interest within the university or community. The

student can spend the semester visiting different

labs, attend talks sponsored by the university, or per-

haps shadow one or more faculty in any area of their

choice. This will require cooperation with faculty or

facilities outside the MNS division, and we envision

the course faculty advisor aiding the students in

obtaining this cooperation. The student will be

required to provide written reports or summaries of

their activities. Three SE skills we see students devel-

oping as result of this course are (1) appreciation for

the role that subject matter expertise plays in

defining and solving complex problems, (2) famili-

arity with other relevant sciences, and (3) the ability

to communicate new knowledge to a wide audience.

Statistics Courses

The statistics courses will be a mix of theory,

methods, and tools. In these courses, students will

be provided with opportunities to collect their own

data and develop more skills in team building,

technical writing, and writing professional reports.

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Project management and benefit–cost analysis will

be integrated into the courses. Projects should be

diverse and will typically involve the following:

1. understanding what is being asked for,

2. conducting some additional research on the topic

through the Internet or other resources,

3. becoming familiar with collecting data,

4. combining statistical methods for a complete

sequential solution to an important problem, and

5. technical writing.

Parts 2 and 4 are integral to the SE process. Students

must become comfortable with seeking out more

information and understanding of problems from

unfamiliar disciplines (pharmaceutics, forensic

science, biology, engineering, etc.) on their own or

in teams. This has been done successfully in intro-

ductory statistics courses. Requiring some of these

projects to be carried out individually and not in

teams will allow the students the opportunity to

solve problems independently of one another in a

structured format and provide independent project

reports. However, we have often encouraged stu-

dents to ask questions of one another and share

information—but analysis, writing, and final sub-

mission is completed individually. There are many

resources available for data and project ideas. One

such repository of information is supported by the

Journal of Statistics Education and can be found at

http://www.amstat.org/publications/jse.

External-sponsor Projects

Use-inspired courses would include projects or

problem scenarios derived from business, industry,

nonprofit, or government entities. The ideal situation

would be to have the entire class work on problems

from one or more of these enterprises, visit the com-

pany site regularly, and provide solutions to the vari-

ous problems they would encounter related to the

course. This would provide the students with

real-world experiences. However, this is rarely a

viable option in courses that have even as few as

10–15 students. However, with technology today it

is still possible to bring in these real-world experi-

ences with a well-defined project for the class. These

projects can be from sponsors that are regional,

national, or international. We have some suggestions

for project development for upper-level courses that

can be conducted involving many of the statistical

engineering phases described earlier.

The instructor in partnership with a sponsor (rep-

resentative) can develop a well-defined problem

encountered in that enterprise. For example, in the

regression analysis and time series course, a real data

set from the sponsor could be provided along with

details about the process under study and what type

of problems the company encounters—and, of

course, the question the sponsor (client) wants

answered. Figure 2 displays Part 2 of a possible

project assignment for the students. The client rep-

resentative would visit the classroom via videocon-

ferencing with the instructor as facilitator. In order

for this to be successful, significant preparation

between the instructor and client representative must

be done before project statement and data are pro-

vided by the client and before the videoconference

takes place; this will maximize the chances that the

project scope is manageable and the students can

complete the project in a matter of weeks. This

type of project connects the statistical tools and

methods with the statistical thinking necessary to

solve difficult problems. All projects will be evalu-

ated by faculty and the representative from the spon-

soring organization. External assessment is

imperative to maintain a high level of quality within

the program.

Student-initiated Projects

Students choose their own project, provide the

scope, collect the data, conduct the analysis, write

a report, and often provide an oral presentation of

their work (poster or as a talk) to be given in class.

It is highly recommended that the students work in

teams, but exceptions for individual projects can be

accommodated. Student-initiated projects can be

easily integrated into any core course. It is not

impossible to have an external-sponsor project and

a student-initiated project completed in a single

course.

Senior Capstone Experience

The senior capstone course provides real-world

experience for graduating seniors with a focus on a

viable solution to a problem from an external spon-

sor (business, industry, government agency, or

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nonprofit organization). This is not an internship.

This will be a team project with a defined scope of

work, deliverables, and oral presentations at least

twice during the semester culminating in a final oral

presentation to the company, faculty, and fellow

capstone course students. In addition, a written mid-

term report and final report will be necessary. The

students’ work will be supervised by a faculty adviser

FIGURE 2 Sample project involving a business, industry, nonprofit, or government partner.

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with feedback provided by the external project spon-

sor. The final product will be read by a committee of

MNS faculty and the project sponsor, with construc-

tive feedback given to the students. The project

sponsor will be someone employed at the

enterprise supplying the problem and play an

integral part in the assessment of the student project

at all stages. This is envisioned to be a very intensive,

all-encompassing experience for the students. The

students will be expected to (this is not an

exhaustive list):

1. develop their knowledge base beyond what they

have done in previous coursework;

2. be innovative in their solutions and recommenda-

tions (think well outside the box);

3. justify their solution to the sponsor using metrics

that are important to the sponsor (metrics stu-

dents may never have heard of before); suggest

possible alternate metrics as well;

4. complete the project as a team, not individually;

5. complete the project by the end of the semester

(project management skills necessary!). If they

do not, they will receive an incomplete (and

because this is a senior project, that can delay

graduation).

This capstone course is modeled after the senior

engineering project course offered by the ISE

department at UIUC. The ISE department at UIUC

has one of the most highly regarded senior engineer-

ing project courses in the nation. The course success-

fully integrates engineering and non-engineering

content with students working on a real-world prob-

lem brought to them by outside industry in the State

of Illinois. It is a semester-long course that challenges

the student in many ways they have not experienced

before. Most companies provide new problems for

the course every semester—a testament to the

department and its dedication to students experienc-

ing real problems. There are many universities that

have this type of senior capstone but very few with

the number of external awards and accolades that

the UIUC-ISE course has received. (For more infor-

mation on the design course and its external awards

visit http://ise.illinois.edu/ge494/index.html.)

We believe that this model and senior experience

concept can be adapted for a statistics curriculum

with a very different student base at the West

Campus of ASU. For example, one UIUC project

dealt with the improvement of a laser-engraving pro-

cess for a Fortune 500 company. The current process

had a 15% roll-to-roll defect rate and the company

was interested in determining which process factors

were responsible for defect rate and how these criti-

cal inputs could be controlled (if at all). To solve this

problem, the team assigned this project had to make

regular visits to the company and talk with pro-

duction line workers, managers, and finance officers

to obtain information about the process and to con-

duct a benefits–cost analysis. The team of three stu-

dents had to research laser-engraving processes

among other areas in order to complete the project.

Their objectives were as follows:

1. Review of the printing process.

2. Analysis of current engraving process. The current

system has many inputs whose effect on the roll

must be understood before alterations can be made.

3. Identify the laser=roll combination to be tested. The

company has different laser and roll systems that

apply different inputs for the final product. A few of

these systems must be selected for in-depth testing.

4. Retrieve and analyze historical data. The company

currently has an extensive database of rolls that

did not comply with specifications. These data

will be analyzed to determine the critical factors

of the output.

5. Setup experiments. The ranges of the laser’s input

parameters will be established and varied in a

series of controlled experimental designs.

6. Run experiments. Using the determined inputs

from the design experiments, rolls will be pro-

duced at the company’s plant.

7. Economic analysis. An economic analysis of the

experiments and the company’s current process will

decide the economic viability of the experiment.

8. Draw conclusions. The results of the experimentswill

be analyzed and follow-up experiments will be

designed based on the results and economic analysis.

9. Give recommendations. The company will be

given a list of recommendations on how to

improve their process using the historical data,

results from the experiments, and the economic

analyses.

The results of this project were positive, although

the team was not able to conduct all of the

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experiments due to restrictions within the company.

The team still provided a detailed analysis of the cur-

rent state of the process, then created experimental

designs involving seven factors each at two levels

with center points and blocking (due to the nature

of the printing). Based on the data that could be

collected, the team determined that the projected

annual savings for the company would be at least

$5,000.00, with a payback period of 6 months and

a return on investment over a 5-year period of

200%. This was an excellent learning exercise for this

team. They experienced researching scientific topics

they knew nothing about, preparing and giving oral

reports to the company sponsor as well as a final

document with all of the objectives addressed. An

equally important aspect of this entire project was

that students learned how to express their conclu-

sions in terms of financial gains and losses for the

company. In turn, the company was given valuable

new insight relating to the laser-engraving process

and recommendations for further studies.

For a senior capstone project to be successful in

general, it will take considerable effort on behalf of

the department faculty to provide the proper scope

of the problem as well as seeking out sponsors in

the area. Because of this significant amount of

upfront work, a dedicated course director may be

needed if the number of statistics majors increases

significantly over time. Students do not need to be

in an engineering discipline to be successful in this

type of course. They must be able to think and

solve problems, similar to an engineer.

Program- and Course-Level

Assessment

Program-level and course-level assessment will be

necessary for meeting the program goals. The ques-

tions posed by Snee (2001), which expand upon

Kirkpatrick’s (1998) four levels of training evaluation,

can be used to assess the program and courses:

1. Did they like it? (Reaction)

2. Did they learn it? (Learning)

3. Did they use it? (Behavior)

4. Did they get results? (Results)

Here, they refers to the students and it refers to the

program’s content and training. The four levels=

questions can be easily applied to the undergraduate

statistics curriculum outlined here. We can use stu-

dent evaluations and exit surveys to answer question

1. We already use assessment methods such as

quizzes, tests, and homework to answer question 2.

Questions 3 and 4 are often much more difficult to

answer. However, if the courses are problem-based,

the questions ‘‘Did they use it?’’ and ‘‘Did they get

results?’’ will be easily answered at the course level.

We envision an additional component to all

courses that can benefit not only the students carry-

ing out a particular project but the rest of the class,

the instructor, and future students. A component of

any course project final ‘‘report’’ can be a video pres-

entation of the students actually conducting the

experiment or any data collection activity that is

involved in their project. With the plethora of

video-recording devices (cell phones, camera=

videos, etc.) video recording has become a very

inexpensive and easy activity. In addition, at univer-

sities and colleges today, file-sharing through the

Web is commonplace with the use of learning man-

agement systems such as Blackboard (http://

www.blackboard.com), Moodle (http://www.moo-

dle.org), and Sakai (http://www.sakaiproject.org).

With cloud computing, we expect file-sharing and

collaboration to evolve tremendously (Tsui 2011).

The videos can be uploaded onto one of the systems

(Blackboard is currently used at ASU). Only students

and the instructor can view the videos, although

other users can be given access if desired.

Video provides a great opportunity for students

and the instructor to offer constructive feedback to

each team on their project. Students can evaluate

the team’s approach to conducting an experiment

or the team’s method of collecting observational

data. The viewing of the video and evaluation of

the team’s work can be done outside of class and

does not have to require a great deal of time on

behalf of the students. Learning management sys-

tems such as Blackboard have capabilities for the

instructor to set up assignments electronically where

students can evaluate each other’s work. The evalua-

tions can be done anonymously if desired by the

instructor. After all team videos have been evaluated,

a document with the compiled evaluations can be

provided to the team. These evaluations can be dis-

cussed in class, which would provide an excellent

way for the students to learn about constructive

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criticism and evaluation. In addition, the instructor

now has numerous examples that can be played

for future students. It should be noted that if videos

of students are to be shared with others, permission

from the students will have to be obtained and in

some situations, institutional review board (IRB)

approval may be needed before the semester course

begins. Video presentations provide an avenue

for additional course-level and program-level

assessment.

Program Advisory Board

We envision establishing an advisory board to over-

see and aid in maintaining a high-quality program in

statistics. The advisory board should consist of pro-

gram alumni as well as representatives from business,

industry, nonprofit organizations, and government

entities. The advisory board can provide input on pre-

paring graduates for the workplace, identifying meth-

ods, techniques, and skills required of our graduates

for employment and graduate studies.

CONCLUSIONS ANDRECOMMENDATIONS

In this article, we have provided our approach to

building an undergraduate statistics curriculum.

There are a number of ways to examine the curricu-

lum we have established. Arguably, we believe the

development of the curriculum itself was an appli-

cation of statistical engineering as defined by Hoerl

and Snee (2010). The components of the curriculum

also involve statistical engineering—moving a stu-

dent from statistics user to a user of statistical thinking

(ASQ 1996). The framework for the statistics program

described in this article, though structured, is also

dynamic and flexible enough to allow faculty com-

plete independence with respect to their content,

projects, and delivery. We have developed some

minimum core competencies and coursework that

we believe can provide the students with the skills

and understanding needed in a continually changing

world. There are many readers who will have alterna-

tive approaches, recommendations, and ideas of how

best to serve the undergraduate statistics major. We

look forward to these alternatives and recommenda-

tions, because it has been our approach to see what

works best in many different fields in many different

ways in order to develop the curriculum that we have.

We look at Figure 1 as a set of tools needed to suc-

cessfully move a student from a user of tools to an

innovative problem solver. We understand that some

students may not be proficient at all three levels. It is

more than likely that students will struggle with one

or more of the core competencies while they are stu-

dents but build these skills as they begin their

careers. Just as with statistics, we do not expect stu-

dents to remember every method, every analysis

approach, or every interpretation they ever saw or

used in a statistics class. We do, however, expect

them to obtain the skills, creativity, and confidence

to approach and solve complex problems as well

as discover new ideas and when they do, they have

enough solid background to recall information and

then develop more knowledge in an area. That is

really our idea of a successful statistics major.

ACKNOWLEDGMENTS

We thank our colleagues in the Mathematical and

Natural Sciences Division at ASU for their input on

focus areas and course development in Natural

Sciences and Applied Computing.

ABOUT THE AUTHORS

Connie M. Borror is a professor in the Division of

Mathematical and Natural Sciences at Arizona State

University West. She earned her Ph.D. in industrial

engineering from Arizona State University in 1998.

Her research interests include experimental design,

response surface methods, and statistical process

control. She has coauthored two books and over

50 journal articles in these areas. Dr. Borror is a Fel-

low of the American Statistical Association and the

American Society for Quality.

Roger L. Berger is a professor and director of the

Division of Mathematical and Natural Sciences at Ari-

zona State University. His research interests include

equivalence testing, exact tests, biostatistics, and stat-

istics education. He is a Fellow of the American Stat-

istical Association and the Institute of Mathematical

Statistics.

Sue Lafond is an academic success coordinator

and faculty associate at Arizona State University.

Melanie Stull has been an academic advising pro-

fessional at ASU since 2006. Currently she works in

the Division of Mathematical & Natural Sciences

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and advises students in applied computing, applied

mathematics, applied statistics, and life sciences.

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