1
$\begingroup$

I want to compare changes in the proportion of fruit purchases over time for a household. For example, in year 1, 4/40 (10%) fruit were apples, in year 2, 12/80 (15%) fruit were apples.

When reporting this in a paper, it feels inappropriate to report the percentage change in a proportion (i.e. "there was a 50% increase in the proportion of apples), but the alternative ("there was a 5 percentage point increase in the proportion of apples") ignores the underlying magnitude. I was curious if there is a good rule of thumb for how to report relative changes in relative quantities (e.g. percentage change of proportions, or percentages, etc).

$\endgroup$
  • $\begingroup$ Differences can be as important as ratios, here and indeed elsewhere. A more subtle point is that many effects are better expressed on a logit scale. Much depends on your readership and analysis. $\endgroup$ – Nick Cox Nov 15 '18 at 18:20
1
$\begingroup$

As a start,

  • I'd recommend to make sure that the denominator is spelled out every time you mention percentages, fractions and relations to avoid confusion.
    This is always recommended, but doubly important here.
  • In similar situations I try to be consistent in which fraction is reported as percentage. So in your example, if I decide to report the fraction of apples in the purchases as percentage, then the change of that percentage is reported e.g. as fold change (if you want to emphasize that it's multiples). IMHO it doesn't hurt to make doubly sure and also report the fractions again:

    the fraction of apples among the fruit purchases by year 2 had increased to 1 1/2 times that of year 1, i.e. from 10 % to 15 %.

    (IMHO e-ink isn't that expensive, and it is far more tedious to try finding out what the reference/denominator is if unexplained percentages or fractions are inconsistently sprinkled throughout a text than to skip over clear but redundant information - the more so as the reader may not find the information as redundant as the author ;-) ).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.