Variables can also be described in terms of how much information they contain. There are four **scales of measurement** that do this. The levels of measurement are important in social research because they have an impact on the types of statistics we can use to simplify and describe our data. As a rule, *always use the most informative level of measurement possible*.

## Nominal Scale

The **nominal scale** consists of a set of categories that provide different names for different categories. The nominal scales does not make any quantitative distinction between categories. Favorite color is an example of a variable measured on the nominal scale. We can name colors, but we cannot make any meaningful quantitative (numerical) distinction between the categories. Does blue and any greater or lesser value than red as a favorite color? No. For this reason, *favorite color* is a nominal variable.

It can be confusing when numbers represent nominal level variables. Sometimes, numbers make convenient names. Think of the numbers on athletic jerseys. So long as these numbers serve only to name a particular player and do not provide any quantitative information (such as better players getting higher numbers) then the scale is still nominal. Do not let the presence of numbers confuse you.

## Ordinal Scale

With the **ordinal scale**, not only are measurements placed in categories (as with the nominal scale), but they are also ranked in order of magnitude. Variable that are rank orders of scores are on the ordinal scale. If someone tells you, “I graduated third in my class,” they are providing an example of an ordinal scale. We do not know the persons precise GPA, but we know he did better than the person graduating fourth in the class and not as good as the person graduating second. Thus, with the ordinal scale, we can put people in *order*, but we do not know the magnitude of the difference between people.

## Interval Scale

An **interval scale** of measurement consists of an ordered set of categories (as with the ordinal scale). In addition, the interval scale specifies that all the intervals are the same size. That is, the spaces between points along the scale are always the same size. Take distance measured in inches for example. The distance between the 2-inch mark and the 3-inch mark on a yardstick is the exact same as the distance between the 35-inch mark and the 36-inch mark. An inch is always an inch, no matter where we find it on the scale.

## Ratio Scale

The **ratio scale** provides all the information that the interval scale does. In addition, the ratio scale provides an absolute zero point. That is, when you reach zero, you do not have any of the variable left.

Annual household income (measured in dollars) is a good example of a common ratio level variable. When you earned zero dollars last year, then you have no income.

Contrast this with temperature measured on a Fahrenheit thermometer. A measurement of zero does not mean that you have no heat left. You can keep going below zero. A Kelvin thermometer has its zero point at absolute zero. Nothing can be colder than zero degrees Kelvin. Thus, temperature, when measured on a Fahrenheit thermometer is on an interval scale. Temperature when measured on a Kelvin thermometer is on a ratio scale.

Note that there is very little difference between the interval scale and the ratio scale. Most statistics that are appropriate for one are appropriate for the other. This is why you will often see both categories with a slash between them in the methodology literature.

Modification HistoryFile Created: 07/25/2018 Last Modified: 07/25/2018

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