South Dakota US senator race 2014 ================================== 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.