A linguistic question about relative and absolute changes

[Clyde Schechter]

It is common in this Forum to encounter questions that relate to relative and absolute changes and the associated terminology when the changing variable is itself a percentage. In English, a change from 50% to 55% is a relative change of 5/50 = 10%, and is an absolute change of 55-50 = 5 percentage points.

Because I am by nature pedantic, I frequently respond to posts that involve this issue. As often as not, the person posing the question appears to be a native speaker of English. But a substantial number of these questions also arise in posts where the author appears to be using English as a second language. It dawns on me that the convention that a relative change is percent, and an absolute change is percentage points may be language specific. And I now worry that in pounding on this terminology, when the reader back-translates my advice into his or her own tongue, the results may be quite incorrect or confusing. I really don't know. I have at least light conversational ability in several other languages, but even in the one I speak almost fluently, I don't know the terms used for these.

The convention is clearly an arbitrary one. There is no reason I can see why it might not have been the rule that percent change means absolute change and some other term is adopted for relative change. For that matter, if I were "redesigning" the English language I would banish the term "percent change" altogether and decree that one always speak specifically either of percent absolute change or percent relative change.

So I have two questions.

1. How are these distinctions handled in other languages commonly in use on this Forum? Are they consistent with how English does it? If not, how difficult is it to translate from the English terminology into these other languages?

2. How did the current English convention come to be?

I realize this is a little off-topic for this forum, as it is neither a question about Stata nor really about statistics. I hope nobody objects.

[Mike Lacy]

Clyde, I think the situation might be even more difficult than you describe, as I've known relatively numerate and literate native English speakers who don't know and use the percent/point convention. (I mean "literate" here in the sense of being careful and precise about language use, and "numerate" in the sense of being sensitive to the absolute/relative chance distinction.) I think of the convention you describe as an available tool but far from universally observed. No need for you to apologize here: If this be pedantry, let us make the most of it. I like your questions, and I'll ask some more knowledgeable sources about 2).

[Andrew Lover]

Pedanticness can (and often does) serve an important purpose, so please continue.

* It is fascinating how arbitrary many conventions are, and how many languages may simply not have specific terms for abs and relative changes.... eg, many languages do not distinguish between blue and green:

https://en.wikipedia.org/wiki/Blue%E...on_in_language

* This question really lies at the boundary of too many disciplines go obviously fall anywhere else, and I absolutely support global inclusions!

(and apologies for going even further off-topic).

[Nick Cox]

(Warning: Mostly digressions.)


I usually do well, or according to your point of view very badly, in pedantry contests.

I looked over at Cross Validated for discussions and found https://stats.stackexchange.com/ques...higher-than-25 and there may be much more to cite,

I don't have answers to Clyde's specific questions. I note that absolute also has the meaning of ignoring sign, so that in Stata terms abs(-42) yields 42 (i.e.. |-42| = 42) -- but that is a separate point.

Terminology in specific fields can dominate for people in those fields. In the Earth sciences absolute dating includes a numerical date while relative dating doesn't (could be within a period, say Jurassic or medieval, so earlier than later periods and later than earlier periods).

I'd link this with discussion of units and dimensions, which are often neglected in statistical science. (So, while it's a lousy account that doesn't tie a discussion of SD and variance to units, explanations of probability density are routinely poor.) See a splendid short paper

Finney, D. J. 1977. Dimensions of statistics. Applied Statistics 26: 285–289. www.jstor.org/stable/2346969.

David Finney (1917-2018) is perhaps best remembered for his work on probit analysis.

In these terms, I'd expect usually absolute to mean a difference using the original units of measurement and relative to mean fractional change (so a dimensionless ratio).

That does not help much when the original units are themselves percents or proportions. I've often seen careful writers talk about percent points to mean a difference but the notation %p mantioned in the first link in this posts is not one I've seen in the wild.

A little related, but occasionally I've seen people use different notation for temperature and change in temperature.

(Three times in literature I've seen puzzlement at coefficients of variation (SD / mean) for Celsius temperatures that were negative -- because the mean was negative. As I recall each author "fixed" the problem by changing to Fahrenheit....) .

[Maarten Buis]

In Dutch and German I have taught a fairly equivalent terminology. My students should not be confused by the English terminology (assuming they still remember what I tried to teach them).

[Paul Dickman]

The same concepts and terminology exist in Swedish. The Swedish words are ”absolut” and ”relativ” . In high school math, Swedes are taught to distuinguish between differences in ”percent” and ”percent units” for relative and absolute differences. Swedes use percent units rather than percent points (used by both Clyde and Nick) in English because it’s the direct translation of the Swedish term (”procentenheter”).