Chapter 1

Chapter 1: Defining and Collecting Data

Objectives

This chapter introduces foundational concepts in statistics related to defining and collecting data. Students will learn about variable types, measurement scales, data collection methods, sampling techniques, data preparation, and survey errors.

• Understanding issues when defining variables

• How to define variables

• Measurement scales

• Data collection methods

• Sampling techniques

• Data preparation and cleaning

• Types of survey errors

Classifying Variables By Type

Categorical and Numerical Variables

Variables are the characteristics or properties that are measured or observed in a study. They are classified into two main types: categorical and numerical.

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

• Numerical (quantitative) variables: Represent counted or measured quantities.

  • 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 a file).

Examples of Types of Variables

Question	Responses	Variable Type
Do you have a Facebook?	Yes or No	Categorical
How many text messages did you send in the past 7 days?	Numerical value	Numerical (discrete)
How long did the mobile update take to download?	Numerical value	Numerical (continuous)

Measurement Scales

Nominal Scale

A nominal scale classifies data into distinct categories in which no ranking is implied. This scale is used for categorical variables where the categories are simply names or labels.

Categorical Variables	Categories
Do you have a Facebook profile?	Yes, No
Type of investment	Growth, Value, Other
Cellular Provider	AT&T, Sprint, Verizon, Other, None

Ordinal Scale

An ordinal scale classifies data into distinct categories in which ranking is implied. The order of the categories matters, but the differences between categories are not necessarily meaningful.

Categorical Variable	Ordered Categories
Student class designation	Freshman, Sophomore, Junior, Senior
Product satisfaction	Very unsatisfied, Fairly unsatisfied, Neutral, Fairly satisfied, Very satisfied
Faculty rank	Professor, Associate Professor, Assistant Professor, Instructor
Standard & Poor's bond ratings	AAA, AA, A, BBB, BB, B, CCC, CC, C, DDD, DD, D
Student Grades	A, B, C, D, F

Interval and Ratio Scales

Both interval and ratio scales are used for numerical variables, but they differ in the presence of a true zero point.

• Interval scale: An ordered scale where the difference between measurements is meaningful, but there is no true zero point (e.g., temperature in Celsius or Fahrenheit).

• Ratio scale: An ordered scale with meaningful differences and a true zero point (e.g., height, weight, age, income).

Variable	Level of Measurement
Temperature (Celsius or Fahrenheit)	Interval
Standardized exam score (e.g., SAT, ACT)	Interval
Height (in inches or centimeters)	Ratio
Weight (in pounds or kilograms)	Ratio
Age (in years or days)	Ratio
Income (in dollars or yen)	Ratio

Summary of Measurement Scales

• Nominal: Categories only, no order (e.g., gender, type of car).

• Ordinal: Categories with order, but no fixed interval (e.g., satisfaction ratings).

• Interval: Ordered, meaningful differences, no true zero (e.g., temperature).

• Ratio: Ordered, meaningful differences, true zero (e.g., weight, income).

Additional info:

• Measurement scales are fundamental for determining appropriate statistical analyses.

• Understanding variable types and measurement scales helps in designing surveys and experiments, as well as in interpreting data correctly.