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    Nobody pays me to write any of the copy on my blog, and should I ever have the good fortune that they do, I will declare it. My main employment is as the owner and principal of The Future Place consultancy. The Future Place provides two key services 1) training and services to industry and academic bodies and 2) consultancy services to companies. The details of the companies I work with are a private matter, but if I blog about any company who has paid The Future Place more than expenses recently (approx. two years) I will mention that they are a client. I hold equity in Virtual Surveys and provide consulting services to them from time to time. I am paid to run courses for a number of trade bodies and over the last few years clients have included ESOMAR, AMSRS, MRS, and MRIA.

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The standard error calculation and the asymptotic normal approximation to the sampling distribution have nothing to do with probability sampling; they come from independence of the observations. Perhaps you meant to say that there is no guarantee that the sampling distribution of, say, a sample proportion is centered on the population proportion, so the coverage of the confidence interval may be incorrect. However, the same applies to any sample with substantial amounts of nonresponse.

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