This article discusses the use of Excel in the
introductory course in statistics in the business school.
An attempt is made to identify how business school programs differ, and how the use
of Excel to work cases or examples can contribute to a business statistics course that is
in keeping with the schools and the instructors learning objectives.
There are possibly more different ways to
teach statistics to business students that any other subject in the business school
curriculum. The business statistics course
can range from a highly quantitative presentation of distribution theory, to a course that
might be described as strategic analysis with data. The observed variations in pedagogy and content
reflect differences among schools and faculty, but also reflect a varying response to
changing technology. This article discusses
some issues that are important in designing the introductory business statistics course,
and presents some ideas for using spreadsheets that may be appropriate in teaching
statistics in the business school.
Designing the Business Statistics Course
No business school course exists in isolation:
they are all part of a larger program. A key
issue in course design is aligning the characteristics of the course with those of the
program in which the course is offered. A
course that does not fit with its program is unlikely to be a very
satisfactory experience for the instructor, or be well received by the students.
The first task in designing any business
school course is, therefore, to understand the nature of the business program. The business school marketplace is highly
competitive and becoming more so, as the major schools compete for the same excellent
domestic and foreign students, and for the attention of the same groups of prestigious
recruiters and major donors. This
marketplace, however, is not homogeneous: there is room for a variety of different kinds
of programs. In marketing terms, business
school programs occupy different positions in this marketplace. The major
schools position their programs in an effort to present a distinctive image and so avoid
direct competition: Chicagos MBA program is very different from Harvard's. Other schools position their programs seeking
differentiation from their major competitors, while avoiding head-to-head competition with
the major schools.
The position a school adopts determines the
appropriate content and pedagogy for its programs. A
course that supports the schools market position is much more likely to prosper than
one that does not. An extreme example will
illustrate this point. One differentiating
feature among programs is quantitativeness which can usually be seen in the
program prerequisites: an MBA program that requires all entering students to have taken a
calculus course is likely to be much more quantitative than one that has no mathematics
prerequisites. A highly quantitative
statistics course in an MBA program that has no mathematics prerequisites is unlikely to
be a great experience for the student or the instructor. Quantitativeness is
one obvious characteristic that differentiates business programs but other positioning
factors are subtler. Here are some other
examples: the extremes of each positional characteristic have been described although many
schools occupy intermediate positions.
management programs take a broad strategic focus without
specializations and aim to produce
programs take a functional focus with concentrations, and emphasize
educating students for early career positions, usually as “staff”.
business schools are people and marketing oriented, tend to be
domestically focused, and are interested in topics such as
entrepreneurism and creativity. Programs
positioned towards global
competition are profit oriented, technologically advanced, and
stress the international arena.
in theoretical programs read
the research literature, understand developing and testing hypotheses,
and talk about management. At
practical schools, students
read the business literature, learn about industries and corporations,
and emphasize implementation and execution.
based programs emphasize “learning”, are academic and scholarly, and
try to teach a body of knowledge about management.
schools see management education more as “training” and emphasize
activities such as report-writing, making presentations, and teamwork.
Analysis orientation emphasizes performing analysis and arriving at
correct solutions, which tends to have a narrow focus.
A Decision orientation
emphasizes making sensible decisions in the face of complexity and
solving real problems, which generally involves integration.
Where a program ends up on these positional
scales emerges as a result of market pressures modified by faculty politics. Faculty will fight hard for positions that match
their personal strengths and interests, which generally favor more
content-based and theoretical programs. If attracting enrollment becomes an issue, schools
will try to find a position that appeals to their particular market. Consequently, program positions are not static but
evolve over time as schools react to both internal and external pressures.
What does this have to do with the design of
the business statistics course? Since about
1990, the poor reaction of the market to overly quantitative MBA programs has
pushed many schools into changing the positions of their MBA programs moving away from theoretical, content, and analysis towards practical, skills, and decision. This positional drift has important
implications for the teaching of statistics.
The Making Statistics More Effective in
Schools of Business (MSMESB) conferences have been held since 1986, and the first such
conference provides support for this positional change.
The conference found that students were best motivated by exposure to real
applications, problems, and cases and suggested that the emphasis in the statistics course
on formal theory be reduced while emphasizing intuitive concepts and applications. Finally, the conference suggested that report
writing and the communication of statistical results received inadequate coverage (Easton, Roberts, and Tiao,
These findings are consistent with a movement in the business schools towards the practical, skills, and decision end of the positional spectrum.
Deciding what is appropriate
statistics instruction in a business school
The first step in course design is to assess
the position of the host program, and then to begin to lay out the general topics to be
included, and select appropriate tools, perhaps including software. Programs that are positioned as theoretical, content and analysis will likely require a
statistics course that presents statistics in a rigorous, analytical way,
perhaps including a fair bit of calculus. I
have no experience teaching such a course, but suspect that the opportunities to use Excel
in this situation are quite limited.
My experience comes from teaching at the
Richard Ivey School of Business and in a number of programs around the world that have all
been positioned towards the practical, skills,
decision, and global business oriented end of the positional
spectrum. These business programs, as do
others, have certain well-understood objectives, and instructors are expected to work
towards these objectives in their courses. The
instructor designing a course can consider these objectives as being in two groups. The first set of objectives might be called the
program objectives, which provide an overall framework under which all courses
and program activities are offered. An
individual course that does not support the program objectives will seem out of place, and
so it is in the interests of each individual course instructor to design a course that
supports these program objectives wherever possible.
For example, a highly quantitative statistics course in a very practical program
will most likely leave the instructor bemoaning the fact that our students
dont know any math, will contribute little to the students practical
ability, and will likely be poorly rated by the students.
The first step in designing a
statistics course is to make a list of the program objectives:
here is one interpretation of a set of program objectives for a practical, skills, decision, and
global business oriented program that would be relevant to the teaching of
statistics. Graduates should
general understanding of the world of business, including major companies, current issues,
personalities, and economic regions,
general understanding of the business functions, and how they interrelate and work
ability to analyze business problems, arrive at sensible solutions, and implement
ability to effectively communicate ideas through formal presentations, written reports,
and group discussions,
ability to receive work presented by others critically and respond appropriately,
understanding of and ability to work in teams.
At first glance, these program objectives may
not seem to have much to do with statistics but the statistics instructor can
contribute to these objectives in many ways. As
some cases or a project on a major international company can help students learn about the
world of business,
examples or cases from marketing, finance or the consulting field can contribute to a
general understanding of the business functions, and how a common understanding of data
can contribute to the functions working together,
or examples where the use of data, supported by statistical analysis, leads to improved
decision-making can develop students ability to analyze business problems and arrive
at sensible solutions. In real world cases,
there is almost always an opportunity to discuss implementation and managing necessary
that provide practice in Excel and/or exposure to functions or features of Excel that are
new to students contribute to developing more general problem analysis skills,
use of a variety of Excel graphical presentation objects (both good ones and bad ones)
helps students understand and learn effective presentation skills,
ability to effectively communicate ideas can be supported by including student
presentations, written assignments, and classroom discussions in the course. Classroom or small group discussions also
contribute to developing the students ability to receive work presented by others
critically and respond appropriately, and
group assignments accompanied by a presentation to the class or a written report,
contribute to developing students teamwork skills.
The second step in designing the course is to
define the course objective: What does the professional statistics instructor
want students to take away from the statistics course as opposed to other
courses in the program? Here is my version of
a statistics instructors wish list.
I would like students taking my statistics course to leave with:
ability to use data to improve their decision making,
ability to present data or results informatively,
ability to analyze data and draw statistically correct conclusions from data,
ability to understand data when it is presented to them, to ask useful (perhaps
probing questions), and to respond appropriately.
Translating these general objectives into
specific statistical skills and abilities, I arrive at the following
statistical topics list. After taking my
course, I would like business students to:
tables and graphs, and be able to create useful and informative presentations of data,
and be able to use, sensible statistics to summarize data including measures of
centralness (mean, median, mode), variability (variance, standard deviation, range) and
distribution (absolute and relative frequencies, histogram, cumulatives),
variability and recognize the existence of uncertainty (or distribution) in all estimates,
and be able to exploit sequence effects in series,
the basic constructs of statistical inference including populations, samples and sample
selection, estimation, and hypothesis testing, and be able to perform statistically
correct estimation and testing, and
correlation and relationships and be able to build and use useful regression models
(simple and multiple, linear and non-linear, and autoregression).
Choice of Pedagogy
Choice of pedagogy follows
identification of course and program objectives. The
course objectives listed above emphasize developing students skills at working with
and using data. These objectives might be
summarized as producing students who can actually do things using statistics, as opposed
to producing students who understand statistical theory.
Usually doing things is taught through practice, and a course with
these objectives should be loaded with problems and examples that students can use to
practice application of the concepts that they are learning.
The program objectives listed
suggest a highly interactive classroom experience with students presenting and discussing
their work, offering their ideas for comment and defending their ideas when they think
they are correct while conceding gracefully when they recognize that they may have erred. The general program objectives can be further
supported if at least some of the problems that the students work on are set in real
companies, deal with current or emerging business issues, and involve leading edge
companies and industries.
The emphasis on real problems
suggests the use of software to facilitate performing the statistical calculations, and
here the instructor has a choice between using special purpose statistical software (such
as SPSS or Minitab) or the general purpose Excel spreadsheet. The case in favor of using Excel includes the
is very widely available in industry and is now quite standard,
is a low set-up cost to using Excel: most students will have used Excel before the course,
is both an immediate and a lasting value to Excel: your
students will be able to use their Excel skills in other courses, and will almost
certainly have access to Excel when they start work,
students' Excel skills supports program objectives of improving students' general problem
analysis skills, and
has instant credibility with students, who recognize Excel as a very widely used and
powerful "number-crunching" device.
There are also some advantages to Excel in
terms of statistical calculations:
Excel statistical functionality is seamlessly integrated with the other Excel functions: it is simply a part of the spreadsheet.
is very good for doing basic data analysis, including graphing and producing tables,
Excel basic statistical functions (including average, standard deviation, median, slope,
intercept) are easily accessible through the function wizard and generally
produce the answers statisticians expect,
Analysis Toolpak adds a great deal of more advanced statistical functionality,
(i.e. one-independent variable) regression is easy if done with Trendlines
although this results in very limited statistics (R2 and regression
It is, however, important to recognize some of
the weaknesses of Excel:
(a few) students will have little prior Excel experience,
makes analysis so easy that some students will do too much analysis,
easier to crunch numbers in Excel than it is to think about why this is being done, or
what value it is,
numbers in Excel is much easier than thinking about softer or more managerial issues,
is poor at handling mathematical formulas, or processing symbols,
function formulas are hidden when using Excel, and
Analysis Toolpak is quite often cumbersome (e.g. Histogram, Multiple
Students who have no prior
Excel experience should be encouraged (or required) to attend an Excel course prior to the
start of the business statistics course: it
is too much to try to teach both Excel and business statistics from scratch in the program
time usually allocated to the statistics course. The
topics list for the Ivey Excel "boot-camp" is attached as Appendix.
There are a number of add-ins
available that enhance the basic statistical functionality of Excel or make it easier to
perform basic statistical operations in Excel. These
include statistical add-ins PHStat, Data Analysis Plus, and MegaStat, as well as @Risk and
Crystal Ball which include simulation capabilities in addition to purely statistical
functionality. I developed my own add-in
called SAM (Statistical Applications Module) originally to help in the classroom, where
I felt the need for one-touch statistical output in order to avoid long quiet spells while
keystroking through standard series of tasks. For
example, often when provided with some sample data that is germane to a decision problem,
it is useful to compute the sample mean, median, variance or standard deviation, maximum
and minimum values, and to look at the distribution (histogram), a sequence plot to check
for sequence effects, and possibly a normal plot to check if the sample is well
approximated by a normal distribution. To
avoid repeating this sequence over and over in the classroom, a single button-click in SAM provides descriptive statistics for a sample
(mean, median, standard deviation, standard error, maximum value, minimum value, and
sample size), with additional buttons providing a default histogram, sequence plot, or
normal plot of the sample. Another single
button provides confidence intervals and prediction intervals from a sample. SAM
proved popular with our students and so we now distribute it to them.
A final important issue is
the prior statistical training of the students. In
the typical required course in business school statistics, there will be students with a
broad range of statistical background. It is
not uncommon to have students with degrees, or near degrees, in statistics mixed up with
artsies who have so far avoided working with numbers and are proud of this
fact. Finding course materials that can challenge those with extensive statistical
prerequisites without overwhelming the artsies can be difficult, but this can
be accomplished through good real world decision-oriented applications and the use of
Excel. Those who understand the statistics
can be challenged by a new area of application, a new statistical analysis tool in Excel,
and can learn by explaining their analysis to others.
At the same time, the neophytes can learn the basic skills and concepts, but
perhaps miss some of the more advanced nuances of the application. Each group should be able to arrive at a decision
recommendation and present their own level of statistical analysis to support their
Introducing Excel Examples into the Course
First, a word about how the classroom might be
set up for an Excel-based session. At the start of class, ask for a volunteer
driver and plug that students notebook into the overhead projector. Choice of driver depends on the class. Early in the course, the chosen driver should be
someone with only moderate proficiency in Excel. Later,
when considerable keystroking is required, for example to build several multiple
regression models, a driver with greater Excel proficiency should be selected. Importantly, the driver should be always working
with his or her own PC and own version of Excel. The
driver should be instructed not to enter anything into the spreadsheet unless instructed
to by the class. This set-up has
a number of advantages, including:
is a highly active learning mode where the students in class are doing things and
contributing, so they keep interested and keep up with developments,
instructor receives instant feedback on where the class is and what the students are
learning, or have learned so far,
instructor does not have to pause while typing at the computer and can concentrate on what
the students are saying,
instructor has no opportunity to demonstrate an inability to type or work the spreadsheet,
kinds of data entry mistakes that the driver makes are typical of the kinds of
mistakes students make, with the result that students learn the processes of correcting
driver is working with their own PC, mouse, and version of Excel which cuts
down on the number of screw-up possibilities, and
who contribute ideas on how to build or improve the model receive quick feed back,
although the instructor needs to moderate the proceedings so that weaker students are not
embarrassed when they suggest something off the wall.
Here are a
few examples to illustrate some basic statistical concepts, and some of the ways Excel
might be used in the classroom in the teaching of statistics.
Last Years Starting Salary Data
Business students are keenly interested in
starting salaries for the schools graduates. The
placement office will probably provide an Excel worksheet that lists starting salary,
bonuses, city, industry, position description, etc. of all of last years graduates
that they know about, sorted by program (mine does).
The data usually covers about three-quarters of the graduating classes. The school probably also publishes
official statistics on starting salaries, most importantly average salaries by
program that are widely quoted.
Prior to the first statistics class, e-mail
this file to the students, including a very general assignment such as: What can you tell
me about starting salaries? At the start of
the class, project this file and ask something like: Where do you want to start? In the next half-hour or so, go where the
students want to go. Usually they will
compute some means [introducing the Excel =average() function], compare them with the
official averages, compute medians [=median()], talk about percentiles, breakout
I-banking, consulting, and marketing and compute separate statistics for these
popular careers. They may also look at
different locations (New York versus Toronto is a popular comparison at Ivey), and discuss
salary variation and ranges.
This exercise serves several functions. It introduces or reviews a number of statistical
concepts in a situation that interests the students keenly, is very real, and from which
they learn a great deal about their future prospects.
Even those students who know the concepts will still learn from this class. The session also reviews Excel and some of its
basic concepts and functionality, and emphasizes the fact the both statistics and Excel
are useful tools to help them, as future managers, understand issues that are important to
Firestone: Pay No Dough if it Doesnt Snow
Understanding statistics is about
understanding variation. Important objectives
of the business statistics course are to introduce students to thinking in terms of
distributions of outcomes, and risk. The Firestone Tire Company case presents a business
situation where point estimates reveal little, but an understanding of the distributions
of the outcomes reveals a great deal. Firestone
is considering a promotion in which buyers of snow tires can claim refunds if there is
little snow. The refund points are expressed
as percentages of average annual snowfall. Understanding
this promotion is all about understanding variation.
Data is provided that enables the risk of the promotion to be assessed for three
Display of the sample data promotes discussion
of important statistical issues about populations, samples, and sample selection. After computing common statistics (mean, median,
standard deviation), and examining distributions (histogram) of snowfall data, a number of
additional statistical issues emerge. Are
there sequence effects? Does the data
"fit" a normal distribution? Once
students are comfortable with the data, the distribution of refunds in each location can
be computed (either from the empirical data or in some cases from a normal distribution
approximation). The distributions reveal that while the expected values look reasonable,
the probability of refunding 100% of the purchase price is quite high. This is, therefore, a risky promotion.
Since the probability of customers receiving
refunds in at least one location is essentially zero, the example also provides an
opportunity for a discussion of the ethics of advertising something which the public might
believe to be possible, but which the company should know is just about impossible.
The Burnhamwood College case is about
admissions to an MBA program. The issue is to
decide what weight to attach to GMAT scores in the admission decision. Data is provided on entering GMAT score and final
MBA program grade point average (GPA) for a sample of students from three consecutive
years. Business students are aware of the
issues, and many are curious about the admissions process, and are very interested in
predicting their own performance in the program. Simple
regression models can be constructed that show a significant but weak (R2 in
the 0.2-0.4 range depending on year) correlation between GMAT and MBA GPA. A predictive model can be constructed that enables
students to enter typical GMATs (their own?) and then interpret prediction
This example enables a number of technical
issues to be covered (I use it as the second class on regression) including the statistics
of the simple regression model, and an example of moderate but significant correlation. The case also illustrates the important point that
the existence of statistically significant correlation does not necessarily lead to a
useful predictive model.
Brent Harbridge Developments
An important management use
of sample data is to provide estimates of probabilities for decision-making purposes. The Brent-Harbridge case merges statistics and
decision analysis. The Chief Executive of a
property development company has to decide how to bid on three upcoming property auctions. Data is available on previous bids at several
different types of property auction, and regression models can be constructed that appear
to provide useful predictive models for winning auction bids. The first exercise for the students is to develop
these regression models. The regression
modeling provides students with practice in model building, including interpreting the
regression statistics, creating category variables, understanding model choice criteria,
and using grouped data. Once useful
regression models are selected, deriving the predictive distribution and recognizing its
normality, together with the properties of the normal distribution, allows computation of
the probability of winning each auction at any bid amount.
Incorporating these probabilities into a decision tree analysis, and including
decision criteria (including expected values) enables a bidding strategy to be derived.
The owner of a convenience
store has been suffering leakage from the till.
Ian Steele has confessed to theft of a small amount, but the financial results of
the store suggest that a much greater amount is missing.
The statistical issue is to try to estimate how much was really stolen and the
period over which the thefts occurred, but the case also provides a rich learning
experience on how theft can be detected in time series data. Many analysis approaches are possible, including
regression with a category variable denoting theft, and hypothesis tests that test key
statistics from the likely theft period with the same statistics from the likely no-theft
period. In the final analysis, a carefully
plotted graph provides as clear a picture of the theft as do the statistics.
Examinations and Grading
Grading an Excel-based course
should be consistent with the pedagogy of the instruction.
This suggests that a reasonable percentage of each students grade be based on
the students contribution to the classes when the examples or cases are discussed.
The written instruments that
match Excel based teaching of statistics most closely are take-home examinations and
in-class cases or examples. Multiple choice
written examinations are problematical since they emphasize content rather
than skills and decision-making ability. The advantage of a take-home examination is that
students can spend the time necessary to perform quite complex analysis or model building,
and then submit a well-written (typed) management report.
Students can work in groups and submit one written report per group, or can work in
groups but submit individual reports. Such a
group take-home examination contrasts nicely with individual in-class examinations based
on one or more cases or problems (where students will have less time to perform the
A combination of carefully
chosen take-home and in-class assignments can contribute to students education in
statistics, but also to the development of their personal individual and group work
skills, writing skills, and their ability to communicate technical material to a general
The use of Excel together
with realistic business examples and exercises can contribute greatly to students
understanding of both business and statistics.
Understanding data, and the
basic elements of descriptive statistics, including graphs and charts, and regression
modeling are identifiable takeaways from the statistics course that have high
added value in a practical, skills, and decision oriented, business program. The ability
to use Excel and the Excel statistical functionality is a skill that students can use
immediately as they enter the workforce, and is seen as valuable by both students and
In addition, the use of real,
relevant, business oriented cases and examples that is facilitated through the use of
Excel, can contribute to students understanding of business and business issues. In
addition to contributing to students education in statistics, cases and examples can
be introduced into the course in a manner that contributes to developing students
presentation, listening, and discussion skills, and also to their writing ability if
written reports are required.
Harbridge Developments, Case 9A98E042, Richard Ivey School of Business, London, Canada.
University (1992), Statistics for Business with
Spreadsheets, Text and Cases, Second Edition, Boyd and Fraser Publishing,
G., H.V. Roberts, G.C. Tiao (1988), Conference Report:
Making Statistics More Effective in Schools of Business, Journal of Business and Economics, Vol. 6, No. 2, pp. 247-260.
Firestone: Pay No Dough if it
Doesnt Snow, Case 9-84-E002, Richard Ivey School of Business, London, Canada
Ian Steele, Case 9A99E009, Richard Ivey School of Business, London, Canada
EXCEL "Boot-camp" Coverage
Rows and columns and sheets:
Change column widths
Menus and Toolbars:
Active object: cell and ranges
Cell/range formats: numbers
format, 0.0000, scientific (E) notation, add decimal and reduce decimal buttons),
date formats and 36000 dates
$ and % buttons
Formulas = +-*/^, calculation order of =A1+B1/C1^2
Strings and string arithmetic (=A&b6&B)
Text and fill colours, change fonts and font size
Bold and Italic and Underline buttons
Cut/Paste cells and ranges
Copy/Paste relative and absolute addressing
Copy/Autofill (pull down one or two cells)
Paste Special Values
Paste Special Transpose
Print: Set Print Area, Print Preview, Fit to
Sort; sorting range and keys.
Bar charts and
Chart items; series, legend, axis labels, titles etc.
Some format options
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