1. LEVELS OF MEASUREMENT

2. OUTLINE Review: Data, Concepts, Variables Levels of Measurement
Issues in Variable Construction

3. STAGE ONE: DEFINING CONCEPTS
STAGE TWO: OPERATIONAL DEFINITIONS
STAGE THREE: LEVELS OF MEASUREMENT

4. OPERATIONAL DEFINITIONS: REVIEW
An operational definition describes how the concept is
to be measured empirically.
Validity is the degree to which the operational definition
measures the characteristic described in the conceptual definition,
and only that characteristic.
Reliability is the extent to which the operational definition is
a consistent measure of the concept—i.e., containing no random
error.

5. COMPONENTS OF MEASUREMENT:
Measurement = Intended characteristic
+ Systematic error
+ Random Error

6. ON THE MEANING OF VARIABLES:
A variable is any characteristic of an individual or unit of analysis. A variable can take different values for different individuals. In other words, it varies.
Specific values for a variable are sometimes known as observations.
Note: Variables are created or invented, not discovered—or assumed.

7. A categorical variable places a unit of analysis into
one of several groups or categories (minimum number of
groups = 2).
A quantitative variable takes numerical values for which arithmetic operations such as adding and averaging make sense.
Urgent reminder: Variables have to vary!

8. Categorical Variables
1. Dichotomous
No-yes
Rich-poor
2. Nominal
East, West, North, South
Democratic, Semidemocratic, Oligarchic, Authoritarian

9. Quantitative Variables
3. Ordinal
First, second, third,… last
Upper, upper-middle, lower-middle, lower
4. Interval (ratio)
Not only rank order, but interval between them
Ratio requires an interpretable zero
The “highest” level of measurement, permitting the most sensitive statistical techniques

10. Two Key Problems 1. Aggregating Indicators 2. Weighting Indicators
Add, multiply….?
Apples and oranges?
2. Weighting Indicators
Are some indicators “more important”?
Weighting cannot be avoided

11. Two Conflicting Principles
Principle #1: Waste no information
Principle #2: Use conceptually appropriate level of measurement, not necessarily the “highest”