The Myth Of The Statistical Tie

-Submitted by David Drumm (Nal), Guest Blogger

This campaign season we’ll hear a lot about “statistical ties.” The “statistical tie” misnomer is used to refer to the situation where one candidate leads another candidate but that lead is within the margin of error (MOE). However, what we’re really interested in is the probability that one candidate leads the other candidate.

Since polling all voters is a costly and time consuming process, a random sample of voters is selected and, based on some assumptions, one can make a probabilistic judgement regarding the outcome of an election. Polling all voters yields the “true” percentage while the random sample can only estimate the “true” value.

Every time a sample is taken, a different (perhaps) estimate of the “true” value is obtained. The estimate plus and minus the MOE is called the confidence interval. A 95% confidence interval says that 95% of the sample estimates will lie within that interval. Also, a 95% confidence interval says that we are 95% certain that the “true” value lies within that interval.

Consider two candidates, Smith and Jones. We want to know what percentage of the voters prefer Smith and what percentage prefer Jones. The “true” percentage is unknown so we randomly sample the population to obtain an estimate. We want to be 95% confident that our estimate lies within the “true” percentage plus-or-minus three points. The figure at the right determines the sample size for different MOEs. Sample sizes usually assume an infinite population and a correction factor is only required when dealing with very small populations.

After our poll of 1067 likely voters, Smith leads Jones 49-46% with an MOE of 3%. Some would call this a “statistical tie” since the lead is within the MOE. However, the following table tells us that Smith’s lead is 84% probable.

H/T: Kevin Drum, Fritz Scheuren.