Once Again: Prefer Confidence Intervals to Point Estimates

Today I saw a claim being made on Twitter that 17% of Jill Stein supporters in Louisiana are also David Duke supporters. For anyone familiar with US politics, this claim is a priori implausible, although certainly not impossible.

Given how non-credible this claim struck me as being, I decided to look into the origin of this number of 17%. I found that this claim is based on numbers reported in a document released by the University of New Orleans Survey Research Center, which I’ll refer to as UNO-SRC going forward. As noted in that document, the question about support for Senate candidates (which includes Duke) was answered by a total of 12 Jill Stein supporters.

If we assume the responses to that survey are like Bernoulli random variables, then a 95% confidence interval for the percentage of Stein supporters who would vote for David Duke would be a range from 2% up to 48%. See this Gist on GitHub for a demonstration of how one might compute that result in R.

Unfortunately, UNO-SRC’s report doesn’t prominently feature this confidence interval, so people are treating the reported number of 17% as more credible than it is. By itself, this is a great example of the reasons why people should almost always focus their attention on confidence intervals rather than point estimates.

But what’s even more striking about this particular example is that the confidence interval for Duke’s support among Stein voters, when combined with other less noisy point estimates from that same survey, suggests that the point estimate is obviously too high.

In particular, the bottom value in the confidence interval places Duke’s support among Stein supporters at 2%. That number is striking because it’s exactly the rate of support that Duke is gathering from the 205 Clinton supporters who responded to the UNO-SRC poll — and it’s also exactly equal to the 2% rate of support found among the 283 Trump supporters that responded to the UNO-SRC poll.

In short, I would argue that a reasonable person would conclude that approximately 2% of Jill Stein’s supporters support David Duke. Making strong claims that Duke’s support is substantially higher than 2% requires evidence that is simply not available.

[Post-Publication Edit] A couple of people have noted that the column containing Senate candidate preference percentages for Stein supporters doesn’t sum to 100%, so it’s possible that the statistical issues I’ve raised don’t even matter: this whole story may derive from nothing more than typo.