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Reflecting the Uncertainty in Design Parameters

I've been thinking about responsive design and uncertainty. I know that when we teach sample design, we often treat design parameters as if they were known. For example, if I do an optimal allocation for a stratified estimate, I assume that I know the population element variances for each stratum. The same thing could be said about response rates, which relate to the expected final sample size.

Many years ago, the uncertainty might have been small about many of these parameters. But responsive design became a "thing" largely because this uncertainty seemed to be growing. The question then becomes, how do we acknowledge and even incorporate this uncertainty into our designs? Especially responsive designs.

It seems that the Bayesian approach is a natural fit for this kind of problem. Although I can't find a copy online, I recall a paper that Kristen Olson and Trivellore Raghunathan presented at JSM in 2005. They suggested using a Bayesian approach to update estimates of the required sample size to reach a targeted number of interviews when you are uncertain about layers of response and eligibility rates.

This is a really nifty idea. I think it has broader application than just setting the sample size. There are a lot of parameters, even cost parameters, about which we lack certainty. The approach might be vary helpful in even thinking about the consequences of this uncertainty (e.g. worst case scenarios, best case scenarios, etc.)

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