South Dakota US senator race 2014 ================================== CANDIDATES OFFICIAL FINAL RESULT RCP MANY-POLL AVERAGE Joni Ernst(R) 52.2 48.0 Bruce Braley(D) 43.7 margin=8.5 45.7 margin=2.3 http://www.realclearpolitics.com/epolls/2014/senate/ia/iowa_senate_ernst_vs_braley-3990.html Significance: If the RCP average was based on polls of 1265+778+701+911+990+647=4709 likely voters, then standard error sqrt(48*52/4709)=0.728 and for the purpose of estimating the Ernst-Braley vote DIFFERENCE this standard error must be doubled to 1.456 percent of the number of voters. So we are 6.2/1.456=4.26 standard deviations off. A perturbation this or more severe is an event of probability 0.00001. As a different error-estimation method, the unweighted mean of these 6 polls Ernst-Braley margins was m = (3 + 0 + 7 + 1 + 1 + 2)/6 = 2.333 and their sample standard deviation was sqrt( ((3-m)^2 + (0-m)^2 + (7-m)^2 + (1-m)^2 + (1-m)^2 + (2-m)^2)/5 ) = 2.503 in which case the official results were 6.2/2.503=2.477 standard deviations off. This is an event of probability 0.007.