A Comparison That's Probably Not Nonmisleading

Imagine this text (from a pro-Obama site) comes your way. What do you do with it?

In February alone, more than 94% of our donors gave in amounts of $200 or less. Meanwhile, campaign finance reports show that donations of $200 or less make up just 13% of Senator McCain's total campaign funds, and only 26% of Senator Clinton's....

Meanwhile, Senator McCain has raised more than 70% of his total campaign funds from high-dollar donors giving $1,000 or more. Senator Clinton has raised 60% of her funds from $1,000-and-up donors.

First, note that this gives February figures for Obama and "total campaign funds" for Clinton and McCain. Second, and perhaps more subtly, two different types of things are being compared. The only thing that's being said about donations to Obama has to do with the percentage of donors who gave $200 or more; for Clinton and McCain, the percentage of total funds is given.

In case the difference isn't clear, let's cook up some highly improbable hypothetical numbers. All of these are consistent with the numbers in this text. Imagine that Obama had 100 donors in February; 95 of them donated $25 each, and 5 gave $2,300 each. And now I'll repeat myself--these figures are improbable, and they're consistent with the text. At any rate, this would give him a February total of $13,875, of which $11,500 came from donors giving $1,000 or more. In other words, 83 percent of this money comes from "high-dollar donors."

The problem is that the percentage of total money from big donors will always be higher than the percentage of total donors who are big (as it were). That's because they give more money. So the comparison made by the text is inherently misleading, unless the Obama contributors in both categories--$200 or less, and more than $200--all gave approximately $200.

So what do you do if text with a comparison like this crosses your desk? I would query it, pointing out the flaws. Some authors will thank you and make a more appropriate comparison (and it might show that the total percentage of money contributed to the author's candidate by large donors is indeed lower than the percentage for the other candidates). Some won't care and will leave it as it is. The truly cynical ones will realize that it's misleading and want to keep it that way. But it's still our job to try to keep them honest, and to make the decent but careless ones look good.

Thank you to H. Luke O'Cephalus for bringing this material, which was found on Brendan Nyhan's blog, to my attention.