Description

Results from opinion polls are presented to us all the time, especially in relation to elections to parliament and other politicial contexts. Frequently, the issue of their accuracy is not mentioned at all or is captured in small print by a phrase such as "Margin of error=3%". What does this mean? Where does it come from? Why and when should we trust it?

The answer is more complex than it initially appears. In introductory statistics courses, students learn about the most basic statistical model of an opinion poll: the idea of simple random sampling from a binary population leads to the binomial model and a simple margin of error calculation. The next level of sophistication is usually to study stratified random sampling and also the multinomial model.

In reality, the situation is much more complicated and there are various factors which introduce biases and affect statistical and non-statistical accuracy. Issues include:

• sampling is often opportunistic and on the basis of availability;
• some selected respondents decline to answer one or more poll questions;
• some respondents may deliberately mislead pollsters;
• poll questions may be phrased differently from the target of interest for the poll, such as an election ballot paper.

Prerequisites

Resources

Wikipedia article on opinion polls.

Wikipedia article on opinion polling for the next UK general election.

Example of a recent YouGov poll report.

Cochran WG (1977) Sampling Techniques. Wiley

Smith TM (1991) Post‐stratification. Journal of the Royal Statistical Society: Series D (The Statistician), 40, pp 315-323.

Peress M (2010) Correcting for survey nonresponse using variable response propensity. Journal of the American Statistical Association, 105, pp 1418-1430.