# Determining statistical significance in election polls from the MoE / confidence interval

I am confused about how to determine statistical significance in election polls. I was taught that overlapping confidence intervals do not necessarily imply a statistically insignificant difference between two values. I was Googling around for an answer, and this article confirming it.

However, this article seems to give a different interpretation. In particular, I'm concerned about a simple yes/no poll question (or Candidate A / Candidate B), and not in the case where there is a 3rd option. The claim the second article makes is that, in this simplified case, one can simply add the confidence intervals and if they overlap, then the difference is not statistically significant i.e Candidate A at 53% and Candidate B at 47% with a +/- 3% MOE is not statistically significant.

The two articles seem to be at odds and I would like to understand why. Is it because, in the case of yes/no polling, the two values are perfectly negatively correlated?

For a yes/no question, the hypothesis of the two options having the same probability is the same as a fixed hypothesis $H_0: p=0.5$. If the a confidence interval for the "yes" option covers 0.5, then the formal test at the same level won't reject the null. By the virtue of the "no" answer being a perfect complement of the "yes" answer, you would have the confidence interval for "no" answer be a mirror reflection of the CI for the "yes" answer around 0.5 (or, to be more precise, anything that can be stated for the probability of the "yes" answer can be stated for 1-probability of the "no" answer). So if the CI for the "yes" answer covers 0.5, then the CI for the "no" answer covers 0.5, as well, and the two CIs overlap. The converse is that if they don't overlap, then neither covers 0.5, the probability of either answer is significantly different from 0.5, and the probabilities of the two answers significantly differ from one another. Of course, this argument hinges critically on you being an American and not being able to imagine elections with more than two candidates.
• The second article makes the argument that if % for B - 2 x MoE $\le$ % for A then the difference is not statistically significant at the bottom of page 2 and top of page 3. – Dan Oct 14 '12 at 13:56