# SCALES OF MEASUREMENT

## Overview

There are a number of ways of measuring things in psychology. Take a moment to think about how you might measure attitudes, anger, language development, attention, or neural processes. These are all research topics that require creative methodology to measure what you're trying to measure (or, in other words...have internal validity). Here, you'll get a brief introduction to four different scales of measurement that are used in a variety of psychological fields. Understanding the differences between these and being able to identify the scale is important in selecting which statistic you use to analyze your data. These are presented in order of precision, from the least to the most precise.

## Nominal Scale

This is basically a way of categorizing or grouping behavior, where the actual numbers are simply labels or identifiers. For example, let's say you were interested in whether a particular display in a store was more effective in inducing males or females in purchasing the product. You could categorize your observations into two categories of 'look but fail to purchase' and 'look and purchase.' You could then assign a '1' to females and '2' to males and record your data in each category. Using '1' for females is completely arbitrary -- it's just an identifier. You could have used 'A,' '2', 'bluk,' or whatever. The point here is that your data are in categories with the number being simply used as a label without any meaning or indicating of order. Usually, nominal data are presented in terms of percentages in each category.

More Examples of Nominal Scale Use

- Counting how many people help someone else in a set-up scene (e.g., someone pretending to be blind cross the street).
- Counting the number of people out of a group of 30 who are relieved from their depression three months after treatment.
- Examining whether extroverts or introverts are more likely to engage in altruistic behavior.
- Asking whether females or males have higher self-esteem.

## Ordinal Scale

Ordinal scales, more precise than nominal scales, are basically sets of rankings. There is no way to know the size of the differences between any data points--just that one is greater than the other. A simple example of this is to arrange a class by height and assign each person a number according to their height ranking. If number 1 is the shortest, all we know is that number 2 is taller, 3 is taller than 2, and so on. We don't know how much taller 1 is from 2, 2 from 3, etc. Not only do we not know the differences, we don't know the actual height of anyone.

More Examples of Ordinal Scale Use

- High school class rankings.
- Social economic class (low, middle, high).

## Interval Scale

Interval scales keep the same rank characteristic as ordinal scales, but interval scales also show the differences between each data point. That is, the difference between 1 and 2 on an interval scale is the same as the difference between 4 and 5, or 8 and 9, or 100 and 101. In other words, the* interval* is the same. Oftentimes in psychology things are measured by a Likert scale in which one rates a statement (often by how much they agree with the statement). Here's an example:

Indicate your agreement with the following statement: |
||||

1 |
2 |
3 |
4 |
5 |

Strongly Disagree |
Disagree |
Neutral |
Agree |
Strongly Agree |

We can generally assume that the interval (psychologically speaking) between 1 and 2 is the same as the interval between 4 and 5. It's very difficult to demonstrate equal intervals here, but it's often assumed in order to analyze data. What an interval *doesn't* mean is that a rating of 4 is twice as great as 2. In fact, the numbers themselves don't tell you anything about the meaning of the numbers themselves. In the scale above, we could have used a scale from -2 to 2, like this:

-2 |
-1 |
0 |
1 |
2 |

Strongly Disagree |
Disagree |
Neutral |
Agree |
Strongly Agree |

It very important to understand that zero doesn't have any meaning in an interval scale. As you can see from the two Likert scales above, the choice of numbers is fairly arbitrary since the scale need not begin with any particular number. What is important (once again) is that the interval between each value on the scale is the same.

More Examples of Interval Scale Use

- IQ Scores. (The difference between an IQ of 92 and 98 is the same as the difference between 130 and 136. Using 100 as the average is arbitrary.)
- Thermometer readings on a Fahrenheit scale. (The difference between 98.6 and 99.6 is the same as the difference between 101.8 and 102.8 -- 1 degree. The value of zero doesn't mean "the absence of heat."

**Ratio Scale**

The most precise and powerful of scales, ratio scales have all the components of an interval scale but here, the zero point is meaningful and means the absence of whatever it is you're measuring. Thus, you cannot have a negative data point using a ratio scale. Not only are the intervals the same but here, you can compare scores in ratio to other scores. That is, a score of 20 is 20 times greater than 1 (20:1) and 10 times greater than 2 (20:2) and twice as great as 10 (20:10). For example, measuring something with a ruler would give you a measure in a ratio scale. Zero literally means "no length" (i.e., that it doesn't exist). Something that is twice inches is half the length of something that is four inches. This is not true in an interval scale.

More Examples of Ratio Scale Use

- A speedometer.
- Walking speed (see Dr. Levine's Pace of Life research by clicking on 'Geography of Time' excerpt).
- Really, any time or length measurement would be on a ratio scale.
- The cost of a cup of coffee