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Margin of Error

There was a debate held yesterday on "Margin of Error" in the presence of nonresponse and using non-probability samples. This is an interesting and useful discussion.

In the best of circumstances, "margin of error" represents the sampling error associated with an estimate. Unfortunately, other matters often... errrrr... always interfere. The sampling mechansim is not easily identified or modeled in the case of nonprobability samples. In the case of probability samples, the nonresponse mechanism has to be modeled. Either of these situations involve some model assumptions (untestable) that are required to motivate the estimation of a margin of error.

One step forward would be for people who report estimated "margins of error" to reveal all of their assumptions in their  models (weighting models for nonresponse or, in the case of nonprobability samples, selection) and describe the sampling and recruitment mechanisms sufficiently such that others can evaluate these assumptions.

Of course, the stronger the assumptions, the less likely the "margin of error" has the specified coverage rate (95% typically) of the population parameter. For example, a single nonresponse adjustment model is a stronger assumption than running several different nonresponse adjustment models, making multiple estimates, and combining that information into a single, broader "margin of error." 

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