To celebrate Election Day, here is a quick Common Science guide to understanding polling results. In order to keep people interested in their coverage, most national news organizations have steadfastly described presidential polling results as “close” without regard to the underlying statistics. The presidential race in not at all close, as laid out in great detail by Nate Silver at fivethirtyeigtht.com who lays out the statistics which undergird the President’s 90+% chance of being re-elected.
To help explain why the race is not close, let me use Ohio as an example. The final poll for Ohio from the well-regarded, Raleigh-based polling firm, Public Policy Polling (PPP), is 52% for Obama and 47% for Romney with a margin of error of +/-3.1%. Many news organizations, CNN in particular, like to describe this situation as “neck and neck”. It’s not.
The data from PPP is graphed in the Bell Curve at the top of the page. The curved blue line shows the probability of a particular result. For example, the chance of President Obama receiving less that 48% of the vote is effectively zero while the chance that he will receive 52% of the vote is approximately 25%.
[Warning: I am about to discuss some calculus, but don’t be frightened.]
While the curve traces out the probability of distinct, single outcomes, you can also calculate the probability of a range of outcomes by integrating the area under the curve for that range. The calculation of interest to statisticians and nervous Obama supporters is, “what is the chance that President Obama will lose Ohio”? To determine that amount, you integrate the area under the curve for all values less than 50%, shown as the little triangle with the red squiggle, and divide by the total area under the curve. This calculation tells you that Governor Romney has a 4.8% chance of winning Ohio giving President Obama a 95% probability of winning. This same analysis applies to many other states as well and explains why Mr. Silver’s calculations shows an almost certain re-election for the President.
By contrast, North Carolina really is neck and neck with the final PPP poll at 49.4% for Romney and 49.2% for Obama. So get out there and vote.
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