Accuracy in Parameter Estimation

Accuracy in parameter estimation (AIPE) is an approach to sample size planning concerned with obtaining narrow confidence intervals. The standard AIPE approach yields the necessary sample size so that the expected width of a confidence interval will be sufficiently narrow. Because confidence interval width is a random variable based on data, the actual confidence interval will almost certainly be wider or narrower than the expected confidence interval width. A modified AIPE approach allows sample size to be planned so that there will be some desired degree of assurance that the observed confidence interval will be sufficiently narrow.

AIPE and modified AIPE are “fixed N” procedures, in that one needs to specify parameters in order to find the sample size, which is then a fixed value. A new version of AIPE, termed sequential AIPE, is not a fixed N procedure but rather is sequential, where sampling of cases continues until a stopping rule is satisfied. Whereas the standard AIPE approach addresses questions such as “what size sample is necessary so that the expected width of the 95% confidence interval width will be no larger than ω,” where ω is the desired confidence interval width, the modified AIPE approach addresses questions such as “what size sample is necessary so that there is γ100% assurance that the 95% confidence interval width will be no larger than ω,” where γ is the desired value of the assurance parameter. Furthermore, sequential AIPE does not ask “What size sample is necessary?” but rather “Is the accuracy of the estimate sufficient for sampling to stop?” This entry further discusses the importance of confidence interval width, the origins and goals of the AIPE approach, and the subsequent development of the sequential AIPE approach.

Confidence interval width is a way to operationalize the accuracy of the parameter estimate, holding everything else constant. Provided appropriate assumptions are met, a confidence interval consists of a set of plausible parameter values obtained from applying the confidence interval procedure to data, where the procedure yields intervals such that (1 − α) 100% will correctly bracket the population parameter of interest, where 1 − α is the desired confidence interval coverage. Holding everything else constant, as the width of the confidence interval decreases, the range of plausible parameter values is narrowed and thus more values can be excluded as implausible values for the parameter. In general, whenever a parameter value is of interest, not only should the point estimate itself be reported, but so too should the corresponding confidence interval for the parameter, as it is known that a point estimate almost certainly differs from the population value and does not give an indication of the degree of uncertainty with which the parameter has been estimated. Wide confidence intervals, which illustrate the uncertainty with which the parameter has been estimated, are generally undesirable. Because the direction, magnitude, and accuracy of an effect can be simultaneously evaluated with confidence intervals, planning a research study in an effort to obtain narrow confidence intervals is considered an ideal way to improve research findings and increase the cumulative knowledge of a discipline.

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