LEVELS OF MEASUREMENT

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

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

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.

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

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.

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!

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

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

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

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