When Is 2 More than 83?

Open almost any newspaper on any day, and you'll find a story about the negative effects of environmental factors. Whether it's about prescription drugs like Vioxx or fetal exposure to toxins in the womb, or frogs with three legs exposed to phthalates, or breast cancer rates among alcohol users, the statistics are almost always unintentionally misrepresented.

One example I saw recently was an op-ed in the St. Paul Pioneer Press. On Nov. 13, 2007, an adoption advocate named Vicky Iacarella wrote a piece called “Affirmation of birth mothers who see adoption as a loving decision,” which endorsed the idea of adoption because it provides a better upbringing for adopted children than they would have had if they had remained with their birth mothers.

The article stated: "Statistics show that children of young, single parents are twice as likely to run away from home; two or three times more likely to be victims of child abuse; and 83 percent more likely to become parents themselves before the age of 18."

Sounds impressive, Vicky. Especially that last one -- 83 percent, wow!

But if the article were comparing each of these conditions in an equivalent way -- where each one was described as "more likely" than its incidence in some non-adopted population -- a bar chart of those likelihoods would look like this, accurately showing that 83 percent is less than twice as likely and way less than the high end of two to three times as likely. But I'd be willing to bet that most people who read that sentence came away with the impression that the “83 percent more likely” figure reflected the largest increase in likelihood.

Part of the problem is that the article mixes the terms "as likely" and "more likely" when those two comparisons are not the same. "More likely" begins from a base number -- the incidence experienced by the control group or general population -- and then tells the increase over that base. "As likely" starts from no incidence for either the control or the experimental group, and then uses the control group as equaling a 100 percent likelihood; the experimental group's incidence is then 100 plus the increased (or decreased) likelihood. So in the adoption example, the numbers would be 183, 200 and 200 - 300 percent as likely.

But since this particular article mixes the two, there's actually no way to know what Vicky means. And the copy editor did nothing to help clarify her words.

In this article, it doesn't really affect the author's argument, which is largely polemical. But in medical research or public health stories, it's often reported that some environmental factor increased the risk of cancer by 30 percent, while some other factor doubled the risk -- and I think it's a disservice to the (admittedly somewhat innumerate) public to let them think that the 30 percent increased likelihood is worse than 100 percent.