# Levels of Measurement

The data we collect have some type of measurement associated with them. This includes data that consists of counts (how many of something there is). In statistics, we classify data into one of four types of measures: nominal, ordinal, interval and ratio. Each of these classifications is described in this article, with examples of each type given.

## Nominal Measures

Nominal data is the “lowest” level of data because it can only be put into categories that have no order to them. Candidates in an election, favorite colors and the cities in which people live constitute nominal data because the candidates, the colors and the cities have no intrinsic order. (They may be ordered after the votes or people are counted, but the categories themselves cannot in any numerically meaningful way.)

A special type of nominal data is dichotomous data. This is when there are only two categories, such as with simple “Yes” and “No” responses or “Male” and “Female” responses.

## Ordinal Measures

Ordinal data is the next higher measurement classification and consists of categories, like nominal data, but with the added characteristic that the categories can be ordered. An example of this type of measurement level is a survey that asks respondents to rate opinion statements using categories such as “Strongly disagree,” “Disagree,” “No opinion,” “Agree,” and “Strongly agree.”

Both nominal and ordinal data consist of counts. That is, there is no real measurement of the data that is possible. Only “how many” are in each category can be determined. The categories themselves cannot be numerically compared (e.g., it makes no sense to say that “Strongly agree” is twice as good as “Agree”). The results can be compared numerically (twice as many people chose “Strongly agree” than chose “Agree”), but the categories cannot. The data is often shown using a histogram or bar chart, such as the one shown here for an employee-survey question. ## Interval and Ratio Measures

Data other than counts fall into two measurement categories, interval and ratio data. Which category a specific measurement falls into depends on the scale that is used. In interval data, the differences between measurements is meaningful but the ratio of measurements is not. In ratio data, which is the highest measurement level, the differences between values and the ratio of values are both meaningful.

One way to determine the levels of measurement is to ask if the scale has a starting point – that is if the value 0 means that none of what is being measured exists. If the answer is yes, then the measurement is at the ratio level. If the answer is no, the measurement is at the interval level. The Fahrenheit temperature scale is probably the most common interval scale because 0oF does not mean there is no temperature. Compare this to weight: A measure of 0 pounds means there is no weight.

Continuing with these examples, the temperature scale is an interval measure because a rise in temperature of, say, 10o has meaning: It is 10o warmer than it was. However, there is no meaning in a temperature doubling, for example, from 10o to 20o or 50o to 100o. (We do not say the temperature doubled. We say the temperature rose.) On a weight scale, though, the difference between two weights has meaning (something that weighs 50 pounds is 40 pounds more than something that weighs 10 pounds) and the ratio between two weights has meaning (something that weighs 50 pounds is five times something that weighs 10 pounds).

If the levels of measurement are of interest to you, you may want to consider pursuing a degree in data science.