The classic application of confidence intervals is political polling: the science of sampling relatively few people to predict the opinions of a large population. However, in the 2010s, the art of political polling — constructing representative samples from a large population — has become more and more difficult.
The Washington Post recently ran a feature about how the prevalence of cellphones was once feared as a potential cause of bias when conducting a political poll… and what’s happened ever since: http://www.washingtonpost.com/blogs/the-switch/wp/2014/11/03/pollsters-used-to-worry-that-cellphone-users-would-skew-results-these-days-not-so-much/.
Previous post: Issues when conducting political polls.
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