To mix units in a quantitative statement is similar to fouling subject-verb agreement or mixing tenses in an ordinary sentence. It happens, but when it appears in print one wonders: where were the editors?
An example is this Times article on voter fraud.
The Times has asserted for months, probably correctly, that voter fraud in the US is minimal and largely a Republican myth. But after reading the first few paragraphs of this carelessly-crafted tract, I began to think fraud proponents might have a point, after all.
The article asserts that the level of credible fraud allegation was “next to none,” whatever that means. It then goes on to explain that there were states in which “somewhat higher” levels of credible fraud were detected: on the order of 20 to 40 “allegations” out of millions “of votes cast. ”
That seems small, it it might very well be small. But “allegations” and “votes cast” are not directly comparable, unless we accept that each allegation corresponds to exactly one vote. To my eye, a level of 20 to 40 reported and credible fraud allegations in one state are high enough to raise genuine concerns.
Like subjects and verbs, compared numbers must agree. For starters, that means their units must agree. Often they don’t however, something I see both professionally and simply reading the paper in the morning.
One way we can defend ourselves against loosy-goosy numerical assertions is simply to look at the numerical units. 20 of what? A million of what? You might be amazed at how often we compare things that really shouldn’t be compared.
Speaking of fraud: in my view we’ve become far too complacent about using the “F” word to describe numerical statements we don’t like. It’s unjustified and unnecessarily inflammatory. True numerical fraud – cooking up numbers – is pretty rare in my experience. On the other hand, sloppiness with numbers is quite common, and we often have to sort that out for ourselves.
In this case the Times, which very often publishes good data-based articles, forgot to numerically as well as grammatically edit their story. Stories based on numbers need both, or many readers will suspect a lack of proper care and attention, as if they saw a headline blaring The Units, They Does Not Agree!