Poll: Nothing new here!

Here's another illustration of why most polling data isn't very interesting -- or, put more formally, why the exciting stuff about polls isn't very valuable, and the valuable stuff isn't very exciting. Let's go to the larger of the morning fishwraps, under the hed "Romney grabs slight edge over Santorum in Michigan primary, 2 polls suggest":

A pair of new polls suggest the race for the Michigan primary has swung to Mitt Romney’s advantage heading into the last weekend before the election – but his lead is a slim one.

Well, maybe. The trouble is, you're every bit as justified in saying "and maybe not." Let's look at what the paper seems to think is the pivot point, between its own poll earlier this week (Santorum 37, Romney 34) and the Rosetta Stone poll conducted Thursday (Romney 36, Santorum 33). Both use pretty small samples of likely voters (400 and 430, respectively), and RealClearPolitics actually manages to correctly calculate the maximum* margin of sampling error at 95% confidence for both. You can, if you want, conclude that Romney has regained -- I think the preferred term is "clawed his way back into" -- the lead.

The logic of significance testing, though, is built around being skeptical of false positives: cold fusion, faster-than-light travel, overnight swings in public opinion, whatever. So you start by proposing a "null" hypothesis: There's no difference not attributable to chance between A and B. Based on our samples, that's a reasonable conclusion about the population of likely voters. Romney's around 35% (samples of 34% and 36%, respectively), and Santorum (37% and 33%) is right around, um ... 35%.

Notice what we're not saying here.** These samples don't show that the candidates are tied. What they show is that "tied, before and after" is as good an estimate as "clawed his way back into contention," and when that's the case, we have an obligation not to pretend we've cured the common cold.

Polling is expensive stuff. (That's a good argument for doing less of it, rather than more of it, given that the bang-to-buck ratio starts to slide downhill at a pretty alarming rate at this point in the season.) It's no fun to be the rimrat who suggests that an appropriate hed for all that investment is "Poll: Nothing new, things are boring." But if you want to play by the rules, that's where you end up.

* The real margin in the Freep poll is more like 4.7 points. For extra credit, calculate the margin of sampling error at 95% confidence for Santorum in the Rosetta Stone poll.
** This means you, Texas visitors!