Percentage change of interval data

Question

My understanding is that the percentage/relative change is applicable/meaningful only with ratio data, and not with interval data. Can you confirm it is right, or correct me if it's wrong?

Answer 1

Yes and no.

Yes

By definition, "interval" data are those for which only the differences in values are supposed to have meaning. (Technically, according to Stevens' original paper: the meaning is unchanged under the action of the group of translations.) That means you should feel free to add any constant you like to the data and that should not change any of your analytical conclusions. Because a percent (or relative) change depends on the base (original value), adding a constant will alter relative changes, demonstrating a relative change is not meaningful.

No

Nevertheless, it is possible to find a useful analysis of a relative change after selecting a specific base for the data. Are you going to reject a potentially insightful or useful result by sticking to your guns and saying "that's not meaningful because these are interval data"? Most likely not. Instead, you will decide that there is something about this particular base that is useful, perhaps meaningful, and you will exploit whatever insights it provides.

I offer a (real) example of this situation at https://stats.stackexchange.com/a/35717/919. The explanation in that case is that temperature, which in many applications will be understood as an interval measurement, is revealed as existing on a ratio scale for certain analyses in physics.

The Lord paper (see below) offers a comparable study wherein nominal data are found to have meaning on an interval or ratio scale.

The moral

The type of a measurement does not, and should not, limit the statistical techniques you might bring to bear on a data analysis.

References

Lord, F. M. (1953). On the Statistical Treatment of Football Numbers. American Psychologist, 8(12), 750–751. https://doi.org/10.1037/h0063675

Stevens, S. S. (1946). On the theory of scales of measurement.