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Abstract:
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Effect sizes are widely used quantitative measures of the strength of a phenomenon, with many potential uses in psychology and related disciplines. In this article, we propose a general theory for a sequential procedure for constructing sufficiently narrow confidence intervals for effect sizes (eg. correlation coefficient, coefficient of variation, etc) using smallest possible sample sizes, importantly without specific distributional assumptions. Fixed sample size planning methods cannot always give a sufficiently narrow width with high coverage probability. The sequential procedure we develop is the first sampling procedure developed for constructing confidence intervals for effect sizes with a prespecified width and coverage probability. We first present a method of planning a pilot sample size after the research goals are specified. Then, after collecting a sample size as large as the estimated pilot sample size, a check is performed to assess if the conditions to stop the data collection have been satisfied. If not, an additional observation is collected and the check is performed again. This process continues, sequentially, until the specified conditions are satisfied.
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