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Beginning of the End … Or the End of the Beginning?

Beginning of the End … Or the End of the Beginning?

Beginning of the End … Or the End of the

Beginning?

The past few years have been challenging for Good Tunes & More (GT&M), a

business that traces its roots to Good Tunes, a store that exclusively sold music

CDs and vinyl records.

GT&M first broadened its merchandise to include home entertainment

and computer systems (the “More”), and then undertook an expansion to take

advantage of prime locations left empty by bankrupt former competitors. Today,

GT&M finds itself at a crossroads. Hoped-for increases in revenues that have

failed to occur and declining profit margins due to the competitive pressures of

online sellers have led management to reconsider the future of the business.

While some investors in the business have argued for an orderly retreat,

closing

stores and limiting the variety of merchandise, GT&M CEO Emma Levia

has decided to “double down” and expand the business

by purchasing Whitney

Wireless, a successful three-store chain that sells smartphones

and other mobile

devices.

Levia foresees creating a brand new “A-to-Z” electronics retailer but

first must establish a fair and reasonable price for the privately held Whitney

Wireless.

To do so, she has asked a group of analysts to identify the data that

would be helpful in setting a price for the wireless business. As part of that

group, you quickly realize that you need the data that would help to verify the

contents of the wireless company’s basic financial statements.

You focus on data associated with the company’s profit and loss statement

and quickly realize the need for sales and expense-related

variables.

You begin to

think about what the data for

such variables would look

like and how to collect those

data. You realize that you are

starting to apply the DCOVA

framework to the objective

of helping Levia acquire

Whitney Wireless.

Chapter Defining and

1 Collecting Data

Tyler Olson/Shutterstock

contents

1.1 Defining Variables

1.2 Collecting Data

1.3 Types of Sampling Methods

1.4 Types of Survey Errors

Think About This: New Media

Surveys/Old Sampling Problems

Using Statistics: Beginning of

the End … Revisited

Chapter 1 Excel Guide

Chapter 1 Minitab Guide

Objectives

Understand issues that arise

when defining variables

How to define variables

How to collect data

Identify the different ways to

collect a sample

Understand the types of

survey errors

Business Statistics: A First Course, Seventh Edition, by David M. Levine, Kathryn A. Szabat, and David F. Stephan. Published by Pearson.

Copyright © 2016 by Pearson Education, Inc.

ISBN: 978-1-323-26258-0

1.1 Defining Variables 11

When Emma Levia decides to purchase Whitney Wireless, she has defined a new

goal or business objective for GT&M. Business objectives can arise from any

level of management and can be as varied as the following:

• A marketing analyst needs to assess the effectiveness of a new online advertising campaign.

• A pharmaceutical company needs to determine whether a new drug is more effective

than those currently in use.

• An operations manager wants to improve a manufacturing or service process.

• An auditor needs to review a company’s financial transactions to determine whether the

company is in compliance with generally accepted accounting principles.

Establishing an objective marks the end of a problem definition process. This end triggers

the new process of identifying the correct data to support the objective. In the GT&M scenario,

having decided to buy Whitney Wireless, Levia needs to identify the data that would be helpful

in setting a price for the wireless business. This process of identifying the correct data triggers

the start of applying the tasks of the DCOVA framework. In other words, the end of problem

definition marks the beginning of applying statistics to business decision making.

Identifying the correct data to support a business objective is a two-part job that requires

defining variables and collecting the data for those variables. These tasks are the first two tasks

of the DCOVA framework first defined in Section GS.1 and which can be restated here as:

• Define the variables that you want to study to solve a problem or meet an objective.

• Collect the data for those variables from appropriate sources.

This chapter discusses these two tasks which must always be done before the OrganizeVisualize,

and Analyze tasks.

Defining variables at first may seem to be the simple process of making the list of things one

needs to help solve a problem or meet an objective. However, consider the GT&M scenario.

Most would quickly agree that yearly sales of Whitney Wireless would be part of the data

needed to meet Levia’s objective, but just placing “yearly sales” on a list could lead to confusion

and miscommunication: Does this variable refer to sales per year for the entire chain or

for individual stores? Does the variable refer to net or gross sales? Are the yearly sales values

expressed in number of units or as currency amounts such as U.S. dollar sales?

These questions illustrate that for each variable of interest that you identify you must supply

an operational definition, a universally accepted meaning that is clear to all associated

with an analysis. Operational definitions should also classify the variable, as explained in the

next section, and may include additional facts such as units of measures, allowed range of

values, and definitions of specific variable values, depending on how the variable is classified.

Classifying Variables by Type

When you operationally define a variable, you must classify the variable as being either categorical

or numerical. Categorical variables (also known as qualitative variables) take categories

as their values. Numerical variables (also known as quantitative variables) have values

that represent a counted or measured quantity. Classification also affects a variable’s operational

definition and getting the classification correct is important because certain statistical methods

can be applied correctly to one type or the other, while other methods may need a specific mix

of variable types.

Categorical variables can take the form of yes-and-no questions such as “Do you have a

Twitter account?” (in which yes and no form the variable’s two categories) or describe a trait

or characteristic that has many categories such as undergraduate class standing (which might

have the defined categories freshman, sophomore, junior, and senior). When defining a categorical

variable, the list of permissible category values must be included and each category

1.1 Defining Variables

Student Tip

Providing operational

definitions for concepts

is important, too, when

writing a textbook! The

end-of-chapter Key

Terms gives you an index

of operational definitions

and the most fundamental

definitions are

presented in boxes such

as the page 3 box that

defines variable and data.

Business Statistics: A First Course, Seventh Edition, by David M. Levine, Kathryn A. Szabat, and David F. Stephan. Published by Pearson.

Copyright © 2016 by Pearson Education, Inc.

ISBN: 978-1-323-26258-0

12 Chapter 1 Defining and Collecting Data

value should be defined, too, e.g., that a “freshman” is a student who has completed fewer

than 32 credit hours. Overlooking these requirements can lead to confusion and incorrect data

collection. In one famous example, when persons were asked by researchers to fill in a value

for the categorical variable sex, many answered yes and not male or female, the values that the

researchers intended. (Perhaps this is the reason that gender has replaced sex on many data collection

forms—gender’s operational definition is more self-apparent.)

The operational definitions of numerical variables are affected by whether the variable being

defined is discrete or continuous. Discrete variables such as “number of items purchased”

or “total amount paid” are numerical values that arise from a counting process. Continuous

variables such as “time spent on checkout line” or “distance from home to store” have numerical

values that arise from a measuring process and those values depend on the precision of the

measuring instrument used. For example, “time spent on checkout line” might be 2, 2.1, 2.14,

or 2.143 minutes, depending on the precision of the timing instrument being used. Units of

measures and the level of precision should be part of the operational definitions of continuous

variables, e.g., “tenths of a second” for “time spent on checkout line.” The definitions of any

numerical variable can include the allowed range of values, such as “must be greater than 0”

for “number of items purchased.”

When defining variables for survey collection (discussed in Section 1.2), thinking about

the responses you seek helps classify variables as Table 1.1 demonstrates. Thinking about how

a variable will be used to solve a problem or meet an objective can also be helpful when you

define a variable. The variable age might be a numerical (discrete) variable in some cases or

might be categorical with categories such as child, young adult, middle-aged, and retirement

aged in other contexts.

Problems for Section 1.1

Learning the Basics

1.1 Four different beverages are sold at a fast-food restaurant:

soft drinks, tea, coffee, and bottled water. Explain why the

type of beverage sold is an example of a categorical variable.

1.2 U.S. businesses are listed by size: small, medium, and large. Explain

why business size is an example of a categorical variable.

1.3 The time it takes to download a video from the Internet is

measured. Explain why the download time is a continuous

numerical variable.

Applying the Concepts

SELF

Test

1.4 For each of the following variables, determine

whether the variable is categorical or numerical. If the

variable is numerical, determine whether the variable is discrete or

continuous.

a. Number of cellphones in the household

b. Monthly data usage (in MB)

c. Number of text messages exchanged per month

d. Voice usage per month (in minutes)

e. Whether the cellphone is used for email

1.5 The following information is collected

Question Responses Variable Type

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