Meta-analysis of last week's Scottish independence polls

As most readers will know, this Thursday (18th September 2014), residents of Scotland will vote in a referendum to decide whether to become independent of the UK. While the No campaign had previously maintained a reasonably healthy lead against Yes, in recent weeks the race has tightened considerably, on the basis of polls of voting intentions. In particular, two polls have now shown larger proportions saying they will vote Yes compared to the proportions voting No. With a flurry of polls conducted in the last week, each with slightly different results, I decided to perform a simple meta-analysis of the poll results, to estimate the current state of play, based on the available evidence.

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Fixed versus random-effects meta-analysis - efficiency and confidence interval coverage

Meta-analysis is a critical tool for synthesizing existing evidence. It is commonly used within medical and clinical settings to evaluate the existing evidence regarding the effect of a treatment or exposure on an outcome of interest. The essential idea is that the estimates of the effect of interest from previous study are pooled together. A choice which has to be made when conducting a meta-analysis is between fixed-effects and random-effects. In this post we'll look at some of the consequences of this choice, when in truth the studies are measuring different effects.

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