In psychology and many disciplines that draw on psychology, data is classified as having one of four measurement scale types: nominal, ordinal, interval, and ratio. The measurement scale indicates the types of mathematical operations that can be performed on the data. Most commonly, measurement scales are used when describing the properties of variables.
The simplest of the measurement scales is nominal. Within nominal data, each observation is assigned a label, and the only conclusions we can draw are based on whether labels are the same or not, and the frequency with which categories (labels) are chosen.
For example, consider data on showing the preferred colors of five people: Blue, Blue, Green, Pink, and Brown. With such data we can count the number of times each color was chosen, and we can compare people based on whether they gave the same response (e.g., the first two people were the same, but the fifth person was different from the first).
Ordinal data is data where there are labels, and there is a meaningful ordering between the labels. For example, consider asking people to rate their happiness, with choices of Unhappy, Somewhat happy, and Happy. If we asked five people to rate their happiness, we might get the data: Happy, Unhappy, Somewhat happy, Happy, Unhappy.
In addition to all the comparisons we were able to perform with the nominal data:
- We can make relative comparisons. For example, persons 1 and 4 are equally happy (based on the data) and both are happier than persons 2, three, and 5.
- When we have two variables that are both ordinal, we can compute nonparametric correlations between these variables.
- We can summarize variables based on their median. For example, the median level of happiness in this data is Somewhat happy.
Interval data is data which can be assigned a numeric value. This allows us to compute quantitative differences between values.
Consider temperature readings recorded in Fahrenheit for five consecutive days, with readings of 31, 33, 39, 32, and 26. The temperature rose by two degrees from the first day to the second, and by six degrees from the second to the third day, which means that the second temperature rise was three times higher than the first. Such calculations are not possible with ordinal and nominal data (e.g., we cannot say with any confidence that the difference between Unhappy and Somewhat happy is the same as the difference between Somewhat happy and Happy).
Interval data’s real power is that it allows the calculation of averages and variance, which are at the heart of most statistical and analysis calculations (e.g., correlation, linear regression).
Data that has a ratio scale is data where it is meaningful to compute ratios. Returning to the temperature data discussed above, with Fahrenheit readings we cannot meaningfully compute ratios. For example, it is not meaningful to say that the day at 39 degrees was 39/31 times hotter than the day at 31 degrees.
By contrast, if five people consumed 10, 20, 5, 3, and 1, cans of Coke in the last week, we can say that the second person consumed twice as much as the first person. The ability to compute ratios is the defining property of ratio scale data. An alternative way to understand this is that if the value of 0 truly means the absence of everything, then the data has ratio scale properties. For example, "0 cans of coke were drunk" means that no coke was drunk, whereas a temperature measurement of 0 degrees does not mean that there was no temperature.
It is important to appreciate that the data measurement scales relate to the properties of the original data itself, and that different scale properties apply to calculations performed on that data. For example, in the case of the nominal data, although the data is nominal, the counts of the number of people to choose each color are ratio-scaled, and thus we can say that twice as many people preferred blue to pink.
The ideas in this article originate in Stevens, S. S. (1959). Measurement. In C. W. Churchman, ed., Measurement: Definitions and Theories, pp. 18-36. New York: Wiley. Reprinted in G. M. Maranell, ed., (1974) Scaling: A Sourcebook for Behavioral Scientists. Chicago, Aldine: 22-41.