Consider this simple math. If 20% of a company’s employees are smokers at baseline, and only 10% are smokers after a company-wide smoking cessation intervention, how much of a decline does this represent?
If your answer is “10%,” you’re wrong, but in good company. Many physicians and a decent swath of the medical literature get this wrong, too. I got it wrong up until a few years ago when a friend of mine in finance set me straight.
The correct answer is either “10 percentage points” or “50%.” Consider the implications. An intervention that reduces smoking by 50% is far more compelling than one that reduces the habit by only 10%.
Now that I am attuned to this important distinction—particularly critical in the comparison of small percentages—it bugs me to notice the error on a regular basis.
I recently came across this conclusion in the referenced BMJ article: “Each 1% reduction in haemoglobin A1c was associated with a 37% decrease in risk for microvascular complications....” At first I was surprised that such a tiny change (only 1%!) could have such a strong impact.
However, given that hemoglobin A1c (HbA1c) is itself expressed as a percentage, this 1% statistic refers to a comparison of percentages. What the authors meant to express was a reduction in HbA1c from, for example, 10% to 9%, which is actually a 1 percentage point difference. (I corresponded with one of the authors to confirm that this is what they meant.) Expressed accurately as a percentage, this decrease in HbA1c from 10% to 9% is actually a reduction of 10%, not 1%.
This is not just annoying semantics. It affects how we think about risk, outcomes, and the efficacy of interventions. Ideally, we ought to make the distinction clear, not only in finance but also in medicine.
Competing interests: No competing interests