The four most recent likely voter polls at RealClearPolitics.com are as follows:
CNN/Opinion Research 9/28 – 9/30 783 LV 3.5 50 47 Obama +3
ABC News/Wash Post 9/26 – 9/29 813 LV 4.0 49 47 Obama +2
Politico/GWU/BattleG 9/24 – 9/27 1000 LV 3.1 49 47 Obama +2
Rasmussen Tracking 9/28 – 9/30 1500 LV 3.0 50 47 Obama +3
They all show Obama with a small lead, but in each the lead is within the margin of error. So, is it more accurate to say based on these results that Obama has a small lead, or more accurate to say that the race is a statistical tie? Nate Silver seems to count polls with Obama leading but within the MOE as Obama leading, but surely if it there was only one such poll it should be considered a statistical tie. So the question is whether aggregating such “statistical ties” can show a lead.
A related question arises in epidemiology as it relates to causation in toxic torts cases. If you have, say, four really good studies that each show a relative risk above two, but the confidence interval at 95% for each of them includes 2.0, should you conclude that the studies suggest a more-than-doubling of the risk, even though arguably none of the studies individually could properly be said to show that?
P.S. No trolling here. I’m genuinely curious how those with statistical training handle such issues.
UPDATE: Comments don’t seem to be working. But thanks to reader Richard Campbell, who sends links to two discussions of when polls should be considered a “tie.” What I get out of these links is that if you take a conservative (in the non-political sense) attitude toward these things, you would say that Romney and Obama are neck and neck. If you are inclined to be more liberal about extrapolating from imprecise statistics, you would conclude that Obama likely has a slight lead (which, by the way, is what I say Rasmussen quoted as saying today, though I can’t find the link). (This, of course, puts to one side any questions about the methodological validity of the polls in question.)
FURTHER UPDATE: With comments not working, I’ve received some private emails, split, as I kind of expected, between those who think that these data, put together in various ways, show a likely Obama lead and those who think that in the absence of having a lot more information that would permit the use of advanced statistical techniques, all we have are four separate inconclusive surveys.