For those who use survey data, the Brexit outcome renews long-standing concerns. Andrew Gelman (Columbia--Statistics) ascribes the difference between most leading surveys (polls) and the Breixt election outcome to five factors (here). Of the five that Andrew identifies, the most troubling (and problematic) is No.2 (what Andrew labels--charitably--as "measurement error"). To be clear, what is implied by "measurement error" in the survey context is that what respondents say they do and actually do (observational data) can vary. To put the point more crassly, some (unknown percentage of) respondents either lie or "delude" themselves. While measurement error always persists as an important threat to data, this threat is particularly acute for survey data. While what to do about this threat isn't obvious, simply ignoring it not a plausible option in most contexts.
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