Can You Spot the Outlier?

(Administrator's Note: The following piece is from guest blogger Carl Gershenson, a graduate student in the Department of Sociology at Harvard. Carl is responding to an interesting post written by journalist Byron York on the supposed racial divide in President Obama's approval ratings. Carl can be reached at cgershen@fas.harvard.edu)

Byron York’s unfortunate blog post is old news by now . Here’s the offending excerpt for those unfamiliar with it:

"On his 100th day in office, Barack Obama enjoys high job approval ratings, no matter what poll you consult. But if a new survey by the New York Times is accurate, the president and some of his policies are significantly less popular with white Americans than with black Americans, and his sky-high ratings among African-Americans make some of his positions appear a bit more popular than they actually are."

Can you spot the racist implications? I sure can. York tries to excuse himself with a lame joke about outliers. And commentary still keeps popping up from wannabe Sir Francis Galtons, who say, “If you’re offended by Byron York’s post, then you’re just statistically illiterate. Blacks are outliers. Haven’t you heard of an outlier?”

I actually consider myself statistically literate, and I'd like to put this outlier excuse to rest. So let’s play “Spot the Outlier.” Say we want to calculate the average number of offspring per male throughout human history. Here’s my sample:

0 5 7 0 2 2 5 1 0 13 250,000

Oops, I sampled Genghis Khan, whose DNA is present in about 8% of Central Asians. I think I can fairly say, “Rulers of the Mongol Horde are outliers.”

Now let’s “Spot the Outlier” for Obama’s approval ratings, where 0 = disapprove and 1 = approve.

1 1 0 1 0 1 1 1 0 0 1 0

Yes, it’s a trick. There is no such thing as an outlier for a binary distribution . For “blacks are outliers” to be true in this sense, some enthusiastic souls on Chicago’s South Side would have to have penciled in a “,000,000” after some of those 1’s. But that didn’t happen.

Ah, but perhaps York’s defenders were arguing that “blacks are outliers” in the sense that our explanatory variable (race) contained outliers, not the response variable (approval). Let’s ignore the fact that average approval ratings are univariate statistics - that is, it makes no sense to talk about average approval ratings having an explanatory variable. Maybe some unusual values in our measurement of race are interfering with our ability to measure the racial composition of the actual American population. So let’s “Spot the Outlier” one last time:

White White White White White White White White White Black

Did you spot the outlier? That extreme observation that is “numerically distant from the rest of the data ”? You know, the observation that makes the American population look a bit more black than it actually is?

Unfortunately for Mr. York, categorical variables (like race) can't have outliers any more than binary variables can. "Blacks are outliers" just doesn't have meaning in within this discussion.

In short, Yorkophiles, there can be no statistically-informed defense of Byron because this is not a debate about statistics. May I suggest that you shift your efforts to Formal Semantics? Because it’s that word--actually--that actually sticks in my craw.