A simple Bayesian analysis of surveys

What share of UK adults gave the right answer to a statistical question?

Anthony B. Masters

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Classical statistics thinks of probability as the long-run frequency of events. The Bayesian approach considers probability as a degree of belief. The language of probability then describes uncertainty in unknown quantities.

The Royal Statistical Society commissioned a survey of the public, asking this question:

  • Question 1: If you toss a fair coin twice, what is the probability of getting two heads?

Opinium conducted this online survey, gathering views of 2,001 UK adults. Researchers weighed responses by gender, age, region, social grade and employment status.

(Image: R Pubs)

Surveys provide estimates, which can differ from true values for many reasons. Researchers use distinct wordings and response options, trying to measure the same concept. Different survey modes, sampling frames, and weights may produce different estimates.

What about the uncertainty in those estimates? Bayesian analyses start with the prior distribution. This distribution represents knowledge before data collection. There were seven response options for the question: 15%, 25%, 40%, 50%, 75%, Other, and Don’t Know.

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Anthony B. Masters

This blog looks at the use of statistics in Britain and beyond. It is written by RSS Statistical Ambassador and Chartered Statistician @anthonybmasters.