Gallup recently released the results of a nationwide poll of registered voters, finding the following:
President Barack Obama is closely matched against each of four possible Republican opponents when registered voters are asked whom they would support if the 2012 presidential election were held today. Mitt Romney leads Obama by two percentage points, 48% to 46%, Rick Perry and Obama are tied at 47%, and Obama edges out Ron Paul and Michele Bachmann by two and four points, respectively.
The story goes on to give the question asked, the basic numerical results, some comparisons to past elections, and a measure of voters' loyalty by party affiliation to these particular candidates. It then offers this "bottom line": "President Obama is at the moment in a rough parity position when registered voters are asked whether they would vote for him in election matchups against four potential Republican candidates. Romney fares slightly better than the other GOP candidates, and Bachmann slightly worse, but these are not large differences."
That very last clause ("these are not large differences") is the closest the text of this release comes to admitting the problem with this generalization. As The Pocket Guide to Critical Thinking explains (pp. 97ff.), there's no way they have good reason to say that Romney leads Obama by 2%, or that Obama leads Bachmann by 4%. The margin of error of the poll is (as Gallup's fine print after the article notes) 4%. So at most this poll shows that it is likely the case that (in a hypothetical Obama-Romney election) Obama has the support of anywhere from 42 to 50% of registered voters vs. Romney's 44 to 52% of registered voters. So Obama could be leading Romney 50% to 44%. Or Romney could be leading Obama 52% to 42%. There's nothing in this poll that would allow us to know anything more precise than that.
Gallup is an old, generally reliable polling organization. This is not a very technical aspect of polling. So they should know better than to say things like this.
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