South Dakota US senator race 2014
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CANDIDATES OFFICIAL FINAL RESULT RCP MANY-POLL AVERAGE
Mike Rounds (R) 50.4 42.2
Rick Weiland (D) 29.5 margin 20.9 30.0 margin 12.2
Larry Pressler (Indep) 17.1 17.2
http://www.realclearpolitics.com/epolls/2014/senate/sd/south_dakota_senate_rounds_vs_weiland-4091.html
Significance:
If the RCP average was based on polls of
908+611+800+730+527=3576
likely voters, then standard error
sqrt(42*58/3576)=0.825
and for the purpose of estimating the Rounds-Weiland vote DIFFERENCE this
standard error must be doubled to 1.651 percent of the number of voters.
So we are 8.7/1.651=5.27 standard deviations off.
A perturbation this or more severe is an event of probability 10^(-7).
As a different error-estimation method, the unweighted mean of these 5 polls
Rounds-Weiland margins was
m = (14 + 11 + 9 + 14 + 13)/5 = 12.200
and their sample standard deviation was
sqrt( ((14-m)^2 + (11-m)^2 + (9-m)^2 + (14-m)^2 + (13-m)^2)/4 ) = 2.168
in which case the official results were 8.7/2.168=4.013 standard deviations off.
This is an event of probability 0.00003.