Let's get marginal

Can you find the probable error (as opposed to statement that you disagree with) in this?

The most recent NBC/WSJ poll... show[s] a plurality (45-43) preferring a Republican-controlled Congress.

--Jonathan Chait, "Republican Health Care Fratricide," New Republic, posted June 30, 2010

OK. What does it mean to talk about "a plurality (45-43)" in a random sample? In this case, it probably means 45 percent of the sample prefer a Republican-controlled Congress and 43 percent prefer a Democratic-controlled Congress. And if we look at the poll Chait links to, that is in fact what it means. But when polling numbers are this close, we need to look at the margin of error. In the linked-to poll it says from the start that the margin of error is ±3.1 percentage points. But the difference between the percentage that prefer Congress (R.) to Congress (D.) is less than the margin of error. Which means that the poll shows no plurality here. This is what some correctly call a statistical dead heat or a statistical tie. Chait is mistaken when he says the poll shows a plurality.

This is something you see a lot of. Consumers (and writers) of news need to watch out for this. As do you and I, my colleagues.