Dcova

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: davidlevine@davidlevinestatistics.com, DavidS@davidlevinestatistics.com

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.

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 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 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 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 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 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 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 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 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 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 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 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.

Copyright of Decision Sciences Journal of Innovative Education is the property of Wiley-Blackwell and its

content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's

express written permission. However, users may print, download, or email articles for individual use.