Defining and Collecting Data: Foundations of Business Statistics

Defining and Collecting Data

Objectives of Data Collection in Business Statistics

Understanding how to define, classify, and collect data is fundamental in business statistics. This topic introduces the key concepts and processes involved in preparing data for analysis.

• Defining Variables: Recognize the importance of clearly specifying what is being measured or observed.

• Measurement Scales: Understand the different ways variables can be measured and categorized.

• Data Collection Methods: Learn how to gather data efficiently and accurately.

• Sampling Techniques: Identify various methods for selecting representative samples.

• Survey Errors: Be aware of common errors and biases in data collection.

Classifying Variables

Types of Variables

Variables are the characteristics or properties that are measured or observed in a study. They are classified as follows:

• Categorical (Qualitative) Variables: Take on values that are categories, such as "yes"/"no" or colors like "blue", "brown", "green".

• Numerical (Quantitative) Variables: Represent quantities that can be counted or measured.

  • Discrete Variables: Arise from a counting process (e.g., number of text messages sent).

  • Continuous Variables: Arise from a measuring process (e.g., time taken to download an app).

Examples of Variable Types

Question	Responses	Variable Type
Do you have a Facebook profile?	Yes or No	Categorical
How many text messages have you sent in the past three days?	Numerical	Discrete
How long did the mobile app update take to download?	Numerical	Continuous

Measurement Scales

Types of Measurement Scales

Measurement scales determine how variables are categorized and interpreted:

• Nominal Scale: Classifies data into distinct categories with no implied ranking. Example: Cellular provider (AT&T, Sprint, Verizon, Other, None).

• Ordinal Scale: Categorizes data with a meaningful order but without consistent intervals. Example: Student class designation (Freshman, Sophomore, Junior, Senior).

• Interval Scale: Ordered scale where differences between values are meaningful, but there is no true zero point. Example: Temperature in degrees Celsius or Fahrenheit.

• Ratio Scale: Ordered scale with meaningful differences and a true zero point. Example: Height, weight, age, salary.

Interval and Ratio Scales Table

Numerical Variable	Level of Measurement
Temperature (Celsius/Fahrenheit)	Interval
Standardized exam score	Interval
Height (inches/centimeters)	Ratio
Weight (pounds/kilograms)	Ratio
Age (years/days)	Ratio
Salary (dollars/yen)	Ratio

Types of Variables: Classification

Hierarchical Structure of Variables

Variables can be organized as follows:

Type	Subtypes	Examples
Categorical	Nominal	Marital Status, Political Party, Eye Color
Categorical	Ordinal	Ratings (Good, Better, Best), Student Grades (A, B, C, D)
Numerical	Discrete	Number of Children, Defects per hour
Numerical	Continuous	Weight, Voltage

Population and Sample

Definitions and Importance

Understanding the distinction between population and sample is crucial for statistical inference:

• Population: All items or individuals of interest in a study.

• Sample: A subset of the population selected for analysis.

Population vs. Sample Table

Population	Sample
All items/individuals about which you want to reach conclusions	A portion of the population
Size 40 (example)	Size 4 (example)

Parameters and Statistics

Key Concepts

• Parameter: A summary value describing a characteristic of a population.

• Statistic: A summary value describing a characteristic of a sample.

Example: If 30% of a sample of mall shoppers used the food court, 30% is the statistic; the true proportion in the population is the parameter.

Sources of Data

Data Collection Activities

• Capturing data from ongoing business activities

• Distributing data compiled by organizations or individuals

• Compiling survey responses

• Conducting designed experiments

• Conducting observational studies

Examples

• Business: Fraud detection from transaction records

• Economics: Forecasting using search engine data

• Marketing: Website effectiveness tracking

• Surveys: Product satisfaction, political polls

• Experiments: Product testing, material selection

• Observational: Focus groups, traffic measurement

Primary vs. Secondary Data Sources

Definitions

• Primary Source: Data collected directly by the analyst (e.g., surveys, experiments).

• Secondary Source: Data collected by others and used for analysis (e.g., census data, published reports).

Sampling Frame and Sampling Methods

Sampling Frame

• A list of items that make up the population.

• Frames can be population lists, directories, or maps.

• Excluding groups from the frame can lead to bias.

Types of Samples

Sample Type	Subtypes	Description
Nonprobability	Convenience	Easy or inexpensive to sample
Nonprobability	Judgment	Expert opinions
Probability	Simple Random	Equal chance for all items
Probability	Systematic	Select every k-th item
Probability	Stratified	Sample from subgroups (strata)
Probability	Cluster	Sample entire clusters

Probability Sampling Methods

• Simple Random Sample: Each item has an equal chance of selection. $P( ext{selection}) = rac{1}{N}$

• Systematic Sample: Select every k-th item after a random start. $k = rac{N}{n}$

• Stratified Sample: Divide population into strata and sample proportionally.

• Cluster Sample: Divide population into clusters, randomly select clusters, and sample all or some items within clusters.

Survey Errors and Ethical Issues

Types of Survey Errors

• Coverage Error: Some groups are excluded from the sampling frame.

• Nonresponse Error: Differences between respondents and non-respondents.

• Sampling Error: Variation due to random sampling.

• Measurement Error: Poor question design or respondent error.

Ethical Issues

• Intentional bias through coverage or nonresponse error

• Failure to report margin of error

• Leading questions or interviewer influence

• Respondent dishonesty

Summary

This chapter covers the foundational concepts of defining and collecting data in business statistics, including variable classification, measurement scales, sampling methods, sources of data, and common errors and ethical considerations in survey research.