Thursday, October 29, 2009

Misleading percentages

When is a fact less than a fact?

When the fact is a percentage of a very small absolute number.

For example, I can state with near certainty that I gave more to philanthropy last year than most other Americans. Indeed, while individuals in general decreased their giving by 2.7 percent (even steeper after inflation), according to the Giving USA Foundation, I increased my giving by 100 percent!

What I'm not revealing, of course, is that my altruism amounted to precisely one dollar in 2007, and to two dollars the next year--a one hundred percent growth rate.

Okay, this is an extreme hypothetical example, but real life examples abound, especially in political campaign literature. A critique of the Michael Bloomberg campaign for Mayor in New York City, for example, cites US Department of Education figures showing declines in violent crime at certain Impact Schools during Bloomberg's reign "as large as 59 percent for major crime...and 33 percent for all crime...." But it adds immediately that "the numbers on which these percentages are based are so low that even very small numerical deceases create large percentage changes."

That's the key point. In one NYC high school, the critique notes, violent crime dropped forty-one percent between the 2004-5 to 2005-6 school years. A phenomenal decline? Not when you realize that the number of incidents in the earlier period was only seventeen, and in the later period ten. To be sure, any decline in violence is good news, but the percentages cited present an unwarranted picture of astounding success by the Administration.

As noted in one of my favorite books, "How to Lie With Statistics" by Darrell Huff (1954), "Percentages offer a fertile field for confusion. And like the ever-impressive decimal they can lend an aura of precision to the inexact."

For journalists covering political campaigns--or anything else--it's good to keep in mind Huff's admonition: "Any percentage based on a small number of cases is likely to be misleading. It is more informative to give the figure itself." (Emphasis added)
Full disclosure: The critique cited above was prepared by the former leader of a tenants organization in which I was an active member.

No comments: