The article describes a framework called DCOVA (Define, Collect, Organize, Visualize, Analyze) for teaching introductory business statistics. The framework presents statistics concepts and methods as a five-step problem-solving process. This helps students see the continuity between topics and applies the process beyond the classroom. Examples show how descriptive statistics and regression analysis fit the DCOVA approach. The framework is intended to improve student learning and retention of statistical concepts.

1. Decision Sciences Journal of Innovative Education
Volume 9 Number 3
September 2011
Printed in the U.S.A.
C©2011, Decision Sciences Institute
Journal compilation C©2011, Decision Sciences Institute
TEACHING BRIEF
Teaching Introductory Business Statistics
Using the DCOVA Framework
David M. Levine† and David F. Stephan
Bernard M. Baruch College (CUNY), 1 Baruch Way, New York,
NY 10010,
e-mail: [email protected], [email protected]
ABSTRACT
Introductory business statistics students often receive little
guidance on how to apply
the methods they learn to further business objectives they may
one day face. And those
students may fail to see the continuity among the topics taught
in an introductory
course if they learn those methods outside a context that
provides a unifying framework.
The DCOVA problem-solving framework that presents discrete
steps to define, collect,
organize, visualize, and analyze data addresses these concerns
while helping to enhance
the perceived value of taking statistics courses.

2. Subject Areas: Content Areas and Statistics.
INTRODUCTION
The introductory business statistics course has the unenviable
reputation among
students as something to survive rather than appreciate. In
“surviving” such a
course, students too often fail to see how the methods they have
learned can
enhance their understanding of other subjects.
When introductory business statistics is taught using a
traditional, method-
by-method approach, students are prone to failing to see the
connection between
descriptive statistics, probability, confidence intervals and
hypothesis testing, and
regression. Failing to make these connections means students
are less likely to
see the applicability of statistical problem solving to other
business content areas.
This is especially unfortunate for two reasons: one, in recent
articles, Baker (2006)
and Lohr (2009) have both noted that statistics and knowing
how to use statistical
applications now are becoming core business skills and two,
Davenport and Harris
(2007) have asserted that using sophisticated quantitative
analyses should be part
of the competitive strategy of any organization. Worse, seeing
an introductory
business statistics course as a series of disconnected topics
would seem to hamper
student retention and, not surprisingly, assessment of what

3. students retain from
the course reveal disappointing results (see Berenson et al.,
2008; Garfield, 2010;
Hollister & Berenson, 2006).
†Corresponding author.
395
396 Teaching Brief
THE DCOVA FRAMEWORK
Presenting the topics of an introductory business statistics
course as part of an orga-
nizing framework for thinking statistically can help students
perceive the continuity
among topics as well as provide them with an explicit problem-
solving method that
they can apply beyond the course. One such framework is the
DCOVA framework
that presents a five-step process as a blueprint for all statistical
problem solving.
In the DCOVA framework, students learn that individual
statistical methods
can each be described as a process to define, collect, organize,
visualize, and
analyze data. Learning that each method consists of the same
series of steps helps
students to begin seeing the continuity of the methods they are
learning, while,
at the same time, showing them the core problem-solving
process that underlies

4. all statistical analysis. The DCOVA framework provides
students with a study
guide that helps them summarize and revisit the methods they
have learned, while
also serving as a blueprint that will help students to apply their
learning beyond
the introductory course. In this way, DCOVA is similar to (and
inspired by) the
prescriptive Six Sigma DMAIC (Define, Measure, Analyze,
Improve, Control)
approach that provides a pathway for quality improvement (see
Gitlow & Levine,
2005). Just as DMAIC provides employees with a framework to
improve quality
within an organization, DCOVA provides students with a
framework for better
retention and enhanced ability to use statistics in the future.
In the DCOVA framework, the words define, collect, organize,
visualize, and
analyze are used as mnemonics to remind the student of the five
steps that form
the process of applying a statistical method. These steps, in
detail, are:
(1) Define the variables that you want to study to solve a
business problem or
meet a business objective.
You always begin by stating the business problem or objective
and de-
termining the variables you need to study to solve the problem
or meet
the objective. Once you have determined the relevant variables,
you must
identify whether each variable is a numerical variable or a
categorical

5. variable. You may also need to know which variable is to be
predicted (as
in a regression analysis) and which variable(s) is to be used to
predict the
variable of interest.
(2) Collect the data from appropriate sources.
In collecting data, you first determine whether you are
collecting the data
from a primary source or a secondary source. If you will be
collecting the
data from a primary source, you then need to determine whether
you will
be conducting a survey or a designed experiment.
(3) Organize the data collected.
After you define your variables and your problem (or business
objective)
and collect your data, you organize your data to prepare for the
later steps
of the process. Typically in an introductory course, you would
organize
the data as a worksheet in which columns are used for each
variable and
rows are used for the data values for each observation.
Organizing data
can also include summarizing data values in simple one-way
and two-way
tables.
Levine and Stephan 397
(4) Visualize the data by developing charts.
You visualize your data using various charts and special

6. displays for
two distinct purposes. Visualizing data helps you to explore and
discover
patterns or relationships in the data (that sometimes are only
seen after
you have organized your data). Visualizing data also helps you
evaluate
the validity of the statistical method used to analyze your data.
(5) Analyze the data by using appropriate statistical methods to
reach conclu-
sions.
You need to have a roadmap for determining which statistical
method to
use to analyze your data. Among the questions that you need to
answer
are: what type of variable are you analyzing, how many groups
are being
compared, are the groups independent, and are you predicting a
variable
based on the values of another variable or variables. Once you
have de-
termined the method to use, analyze also means to think about—
and not
just to report—the results of a statistical method.
The following represents a brief description of using the
DCOVA approach
in descriptive statistics and in regression.
Descriptive Statistics
You have been hired to assist clients who wish to invest in
mutual funds. Since
mutual fund returns have exhibited a great deal of volatility in
recent years, you

7. have decided to focus on funds that invest in different types of
bonds.
Define
You must define your variables and your business objective.
You first decide that
you will focus on intermediate government funds and short-term
corporate bond
funds. Your business objective is to determine whether there is
a difference in the
returns of these funds in the last year, last 3 years, and last 5
years.
Collect
Data from a sample of bond funds can be extracted from the
Business Week Mutual
Fund Scoreboard at bwnt.businessweek.com/mutual_fund/index.
Organize
The data are entered into an Excel worksheet with each variable
occupying a sepa-
rate column and each bond fund in a separate row. Tables such
as one-way summary
tables, two-way tables, multidimensional tables, and frequency
distributions can
be developed.
Visualize
A variety of different charts can be constructed to enable you to
describe the bond
funds and examine whether differences exist between the
intermediate government

8. funds and short-term corporate bond funds.
398 Teaching Brief
Analyze
This phase is the culmination of the DCOVA approach, since
your ultimate goal is
to solve a business problem or meet a business objective. In a
descriptive analysis,
you would examine the tables you developed in the organize
phase and the charts
you constructed in the visualize phase and use them along with
pertinent descriptive
statistics to reach conclusions about any differences that may
exist in the returns
of the intermediate government funds and short-term corporate
bond funds.
Regression
The owner of a moving company located in New York City
typically has his most
experienced manager predict the total number of labor hours
that will be required
to complete an upcoming move.
Define
The owner has the business objective of developing a more
accurate method of
predicting labor hours. The variable of interest was defined as
the labor hours
required for each move. Travel time from the origin location to

9. the destination was
to be eliminated from consideration. The primary variable that
impacts labor hours
is the square footage of the contents being moved. Other
variables to be considered
are the number of pieces of large furniture to be moved and
whether the origin or
destination are apartment buildings that have elevator service.
Collect
Data were collected for 36 moves in which the origin and
destination were within
the borough of Manhattan in New York City and in which the
travel time was an
insignificant portion of the hours worked.
Organize
The data were organized in an Excel worksheet.
Visualize
Since you are interested in exploring the relationship between
the labor hours and
other variables, you can construct scatter plots of labor hours
with the square feet
to be moved, the number of pieces of large furniture, and
whether the origin and/or
destination is an apartment building that does not have an
elevator.
Analyze
The variable that you want to predict is labor hours. You can
use least squares

10. regression analysis for predicting this variable since it is a
numerical variable. You
might begin by using the square feet to be moved in a simple
linear regression
model, evaluate its fit and the validity of its assumptions before
considering other
variables. In addition to the scatter plots constructed in the
visualize phase, you
will need to construct residual plots to evaluate the validity of
the assumptions and
normal probability plots or histograms of the residuals. Then, if
appropriate, you
can develop multiple regression models to predict the labor
hours.
Levine and Stephan 399
More details concerning examples of applying the DCOVA
framework in an
introductory business statistics course are available at
http://davidlevinestatistics.
com/dcova.
CONCLUSIONS
Students in the introductory business statistics course often
experience a lack of
continuity between the topics covered in the course and suffer
limited retention
of what they have learned. The DCOVA five-step process
provides an organizing
framework that can improve the perception of continuity and
enhance student
retention while providing a blueprint for applying statistical

11. learning beyond the
statistics classroom.
REFERENCES
Baker, S. (2006, January 23). Why math will rock your world:
More math geeks are
calling the shots in business. Is your industry next? Business
Week, 54–62.
Berenson, M. L., Utts, J., Kinard, K. A., Rumsey, D. J., Jones,
A., & Gaines, L. M.
(2008). Assessing student retention of essential statistical ideas:
Perspectives,
priorities and possibilities. The American Statistician, 62, 54–
61.
Davenport, T., & Harris, J. (2007). Competing on analytics: The
new science of
analytics. Boston: Harvard Business School Press.
Garfield, J. B. (2010). Assessment resource tools for improving
statistical
thinking: The CAOS test. Retrieved February 7, 2010, from
https://app.
gen.umn.edu/artist/caos.html
Gitlow, H., & Levine, D. M. (2005). Six sigma for green belts
and champions.
Upper Saddle River, NJ: Financial Times/Prentice-Hall.
Hollister, K. K., & Berenson, M. L. (2006). Framework for
retention assessment
in an AACSB international-accredited business school: A case
study in busi-
ness statistics. Proceedings of the Annual Meeting of the

12. Decision Sciences
Institute. San Antonio, TX, November.
Lohr, S. (2009, August 6). For today’s graduate, just one word:
Statistics. The New
York Times, A1, A3.
David M. Levine is Professor Emeritus, Statistics/CIS
Department, Baruch Col-
lege (CUNY). He is nationally recognized as a leading
innovator in statistics
education and is the coauthor of 14 books, including Statistics
for Managers Using
Microsoft Excel, Basic Business Statistics: Concepts and
Applications, Business
Statistics: A First Course, Even You Can Learn Statistics, Six
Sigma for Green
Belts and Champions, and Statistics for Six Sigma Green Belts .
He has given nu-
merous talks at Decision Sciences, American Statistical
Association, and Making
Statistics More Effective in Schools of Business conferences.
He has also received
several awards for outstanding teaching from Baruch College.
400 Teaching Brief
David F. Stephan is an independent instructional designer who
taught Informa-
tion Systems topics for over 20 years at Baruch College
(CUNY). While at Baruch
College, he pioneered the use of, and oversaw the
implementation of personal
computer classrooms; devised interdisciplinary multimedia

13. tools; and created ped-
agogical techniques for presenting computer applications in a
business context. The
developer of PHStat2, the Pearson Education statistics add-in
system for Microsoft
Excel, he has coauthored several books with David M. Levine.
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