Arkansas senator race 2014 =========================== http://www.realclearpolitics.com/epolls/2014/senate/ar/arkansas_senate_cotton_vs_pryor-4049.html Official final results: Tom Cotton(R) 56.5 Mark Pryor(D) 39.5 ; margin = 17.0 RCP many-poll average: Tom Cotton(R) 48.2 Mark Pryor(D) 41.2 ; margin = 7.0 Poll Date Sample MoE Cotton (R) Pryor (D) Spread Final Results -- -- -- 56.5 39.5 Cotton +17.0 RCP Average 10/16 - 11/1 -- -- 48.2 41.2 Cotton +7.0 PPP (D)* 10/30 - 11/1 1092 LV 3.0 49 41 Cotton +8 Rasmussen Reports 10/27 - 10/29 967 LV 3.0 51 44 Cotton +7 The Arkansas Poll 10/21 - 10/27 568 LV 4.1 49 36 Cotton +13 NBC News/Marist* 10/19 - 10/23 621 LV 3.9 45 43 Cotton +2 CBS News/NYT/YouGov 10/16 - 10/23 1567 LV 4.0 47 42 Cotton +5 Talk Business Poll* 10/15 - 10/16 2075 LV 2.2 49 41 Cotton +8 Rasmussen Reports 10/13 - 10/15 940 LV 3.0 47 44 Cotton +3 Significance: If the RCP average was based on polls of 1092+967+568+621+1567=4815 likely voters, then standard error sqrt(48*52/4815)=0.72 and for the purpose of estimating the Cotton-Pryor vote DIFFERENCE this standard error must be doubled to 1.44 percent of the number of voters. So we are 10/1.44=6.94 standard deviations off. A perturbation this or more severe is an event of probability 2*10^(-12). As a different error-estimation method, the unweighted mean of these 5 polls Cotton-Pryor margins was m = (8 + 7 + 13 + 2 + 5)/5 = 7.000 and their sample standard deviation was sqrt( ((8-m)^2 + (7-m)^2 + (13-m)^2 + (2-m)^2 + (5-m)^2)/4 ) = 4.062 and if we use that sigma then the official results were only 10/4.062=2.462 standard deviations off. This is an event of probability 0.007.