Statistics Definitions > Interval Scale

## What is the Interval Scale?

A interval scale has measurements where the **difference between values is meaningful.** In other words, the differences between points on the scale are measurable and exactly equal. For example, the difference between a 110 degrees F and 100 degrees F is the same difference as between 70 degrees F and 80 degrees F.

*Dates *are also measured on an interval scale. For example, there’s 100 years between the 20th and 21st, and also the 21st and 22 centuries. Dates illustrate a major problem with interval scales: **the zero is arbitrary.** Year zero doesn’t exist in the A.D. system (which starts at year 1) but the Buddhist and Hindu calendars include it. Arbitrary zeros are one reason why you can’t say that “the 10th century is twice as long as the fifth century.” This leads to another issue with zeros in the interval scale: Zero doesn’t mean that something doesn’t exist. For example, **the year 0 doesn’t imply that time didn’t exist.** And similarly, a temperature of zero doesn’t mean that temperature doesn’t exist at that point. Arbitrary zeros (and the **inability to calculate ratios** because of it) are one reason why the ratio scale — which *does *have meaningful zeros — is sometimes preferred.

## Interval Variable

An interval variable is a variable that falls on the interval scale. It is a type of continuous variable. Technically (and this is really splitting hairs), it isn’t the variable itself that is interval, but rather the scale itself. For example, a variable of 90^{0}F belongs to the interval scale; you wouldn’t actually define “90 degrees” as being an interval variable.

## Other Measurement Scales.

The interval scale is one of four scales used in stats. The other three are:

**The Ratio Scale**: Encompasses most measurements in physics and engineering like mass and energy as well as variables like height and weight. Ratio scales are very similar to interval scales. However, they also have meaningful zeros (zero weight means that weight does not exist). Degrees Celsius and degrees Fahrenheit are*not*ratio scales, because a temperature of 0 does not mean that “temperature doesn’t exist.” The Kelvin temperature scale on the other hand*is*a ratio scale, because zero Kelvin means an absence of heat.- The
**Nominal Scale**: Data that can be put into categories. This set of data has no meaningful differences between values. In other words, you can’t put a value between the categories of “cats” and “dogs.” - The
**Ordinal Scale**: Items that can be placed in rank order (like first, second, third). The differences between values are also not meaningful in this scale. Imagine you placed first in a contest. There’s no way to see how far second place was behind you. Even if you*could*measure it (say, in seconds), it’s highly unlikely that third place would have the same difference in seconds, and virtually impossible (in the billion billions) that all the contestants were equally far apart.

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