﻿ Scales of Measurement Graziano & Raulin
Research Methods (8th edition)

## Scales of Measurement

One of the most influential distinctions made in the field of measurement was Stevens' (1946, 1957) classification of scales of measurement. He described nominal, ordinal, interval, and ratio scales of measurement, which are briefly defined below. A more detailed discussion of these scales can be found in Chapter 4 of the text.

• Nominal: Nominal scales are naming scales. They represent categories where there is no basis for ordering the categories.
• Ordinal: Ordinal scales involve categories that can be ordered along a dimension. However, we have no way of knowing how different the categories are from one another. We state the latter property by saying that we do not have equal intervals between the items. Rankings also represent ordinal scales, because we know the order but do not know how different each person is from the next person.
• Interval: Interval scales are very similar to standard numbering scales, except that they do not have a true zero. That means that the distance between successive numbers is equal, but that the number zero does NOT mean that there is none of the property being measured. Many measures that involve psychological scales, especially those that use a form of normal standardization (e.g., IQ), are assumed to be interval scales of measurement.
• Ratio: Ratio scales are the easiest to understand, because they are numbers as we usually think of them. The distance between adjacent numbers are equal on a ratio scale and the score of zero on the ratio scale means that there is none of whatever is being measured. Most ratio scales are counts of things.

The most important reason for making the distinction between these scales of measurement is that it affects the statistical procedures that you will use in describing and analyzing your data.

In this unit, we will be presenting dozens of examples of measures at each of these levels of measurement, along with some exercises to help you to refine your understanding of these distinctions. We recommend that you complete the exercises since the best way to learn anything is to actively process the information by using it to solve real-life problems.

## Examples of Each Scale of Measurement

Listed below are several examples of each scale of measurement. We have focused on frequently used psychological variables to help illustrate what each of the scales represent. We have tried to provide a wide variety of examples to help make these distinctions clear for you.

### Nominal Scale Examples

• diagnostic categories
• sex of the participant
• classification based on discrete characteristics (e.g., hair color)
• group affiliation (e.g., Republican, Democrat, Boy Scout, etc.)
• the town people live in
• a person's name
• an arbitrary identification, including identification numbers that are arbitrary
• any yes/no distinctions
• most forms of classification (species of animals or type of tree)
• location of damage in the brain

### Ordinal Scale Examples

• any rank ordering
• class ranks
• social class categories
• order of finish in a race

### Interval Scale Examples

• scores on scales that are standardized (i.e., with an arbitrary mean and standard deviation, usually designed to always give a positive score)
• scores on scales that are known to not have a true zero (e.g., most temperature scales except for the Kelvin Scale)
• scores on measures in which it is not clear that zero means none of the trait (e.g., a math test)
• scores on most personality scales based on counting the number of endorsed items

### Ratio Scale Examples

• time to complete a task
• number of responses given in a specified time period
• weight of an object
• size of an object
• number of objects detected
• number of errors made in a specified time period
• proportion of responses in a specified category

## Exercises

Listed below are a number of exercises designed to familiarize students with the classification of measures using Stevens' classification system. For each of the measures listed, determine what scale of measurement most closely approximates the measure as described. Some of the examples are deliberately ambiguous. To find out the correct answer, click on the word answer at the end of the description of the item.

1. the number of questions asked by a customer during a simulated encounter with a salesperson answer
2. the religious group that one affiliates with answer
4. the score on a 35-item scale of ambivalence answer
5. the rank of a person's salary within the company answer
6. rank order based on IQ score in the sample answer
7. the square footage of each participant's house or apartment answer
8. the size of the cerebellum expressed as a volume answer
10. the time it takes for a couple to resolve a custody issue during court ordered mediation answer
11. score on the Beck Depression Inventory (a pencil and paper depression scale) answer
12. ratings of anger shown by those involved in courtroom testimony answer
13. the number of pound lost during a six-week diet answer
14. the proportion of weight lost during a six-week diet answer
15. the heart rate of the participant answer
16. the percent shift in heart rate over baseline during an emotionally demanding task answer