intervalscaled

Interval scaled data, or interval scale data, refer to measurements organized on a scale with equal intervals between adjacent values and an arbitrary zero point. This means that the difference between any two values is meaningful and consistent, but the zero does not represent an absence of the quantity being measured. Consequently, while one can meaningfully compare differences and compute averages, ratios are not generally meaningful.

A common example is temperature on the Celsius or Fahrenheit scales. The interval between 20 and 30 degrees is the same as between 70 and 80 degrees, but 0 degrees does not denote “no temperature.” Other interval scaled measures can arise in psychological testing, such as certain standardized test scores, where the distance between scores is interpretable but a score of zero does not imply the complete absence of ability or trait.

In statistical practice, interval data support many standard descriptive and inferential methods, including computing means, standard deviations, and performing correlation and linear regression analyses. They are distinguished from ordinal data, where only order is meaningful, and from ratio data, which have a true zero and allow meaningful statements about ratios. For interval data, some multiplicative or ratio-based interpretations (such as “twice as large”) are not valid, though linear transformations preserve the interval structure.

Transformations that preserve interval properties are linear of the form X' = a + bX with b > 0. Such transformations change the unit and origin but retain equal intervals and the interpretability of differences.

See also: measurement scales, nominal, ordinal, ratio.