Collaborative Research: Using Prior Kurtosis Information to Improve Confidence Intervals for Standard Deviations

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This research will apply meta-analysis and the Theil-Goldberger mixed estimation method to improve the standard error of a sample variance. The study will show how kurtosis information from previous studies can be combined using a new meta-analytic kurtosis estimator and that this estimator is less biased than the standard meta-analytic kurtosis estimator. The study also will show how to apply the Theil-Goldberger method to mix a meta-analytic kurtosis estimate with a sample kurtosis estimate to obtain an asymptotic distribution-free standard error of a sample variance. The asymptotic distribution-free standard error will then be used in three basic confidence intervals for standard deviations: 1) a confidence interval for a single standard deviation, 2) a confidence interval for a ratio of two standard deviations in independent-samples designs, and 3) a confidence interval for a ratio of two standard deviations in paired-samples designs. This research will examine the small-sample coverage probabilities of the three basic confidence intervals for several sample sizes and a wide range of realistic distributions.Confidence intervals for a standard deviation or a ratio of standard deviations can be used to answer fundamental questions in psychometrics, behavior genetics, and quality control. Currently available methods are based on unrealistic assumptions, such as normality or equal kurtosis, and can perform poorly if these assumptions are violated in subtle ways that would be difficult to detect using standard diagnostic tools. The results of this study will provide scientists with a new set of statistical tools that can be used to assess variability in a wide range of applications and can be expected to perform well under realistic conditions.