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# Scales and Scaling

This chapter is about building and using composite measures. I’ll cover four kinds of composite measures: (1) indexes, (2) Guttman scales, (3) Likert scales, and (4) semantic differential scales. At the end of the chapter, I’ll cover a few other interesting scales. First, though, some basic concepts of scaling.

## SIMPLE SCALES: SINGLE INDICATORS

A scale is a device for assigning units of analysis to categories of a variable. The assignment is usually done with numbers, and questions are used a lot as scaling devices. Here are three typical scaling questions:

1. ‘‘How old are you?’’

You can use this question to assign individuals to categories of the variable ‘‘age.’’ In other words, you can scale people by age. The number that this first question produces has ratio properties (someone who is 50 is twice as old as someone who is 25).

2. ‘‘How satisfied are you with your classes this semester? Are you satisfied, neutral, or unsatisfied?’’

You can use this question to assign people to one of three categories of the variable ‘‘satisfied.’’ That is, you can scale them according to how satisfied they are with their classes. Suppose we let satisfied = 3, neutral = 2, and unsatisfied = 1. Someone who is assigned the number 3 is more satisfied than someone who is assigned the number 1. We don’t know if that means 3 times more satisfied, or 10 times, or just marginally more satisfied, so this scaling device produces numbers that have ordinal properties.

3. ‘‘Do you consider yourself to be Protestant, Catholic, Jewish, Muslim, some other religion? Or do you consider yourself as having no religion?’’

This scaling device lets you assign individuals to—that is, scale them by—categories of the variable‘‘religious affiliation.’’Let Protestant = 1, Catholic = 2, Jewish = 3, Muslim = 4, and no religion = 5. The numbers produced by this device have nominal properties. You can't add them up and find the average religion.

These three questions have different content (they tap different concepts), and produce numbers with different properties, but they have two very important things in common: (1) All three questions are devices for scaling people; and (2) In all three cases, the respondent is the principal source of measurement error.

When you use your own judgment to assign units of analysis to categories of a scaling device, you are the major source of measurement error. In other words, if you assign individuals by your own observation to the category ‘‘male’’ or ‘‘female,’’ then any mistakes you make in that assignment (in scaling people by sex) are yours.

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