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Date of Award
Education Evaluation and Research
Nonnormally distributed data is common in practice and is often a concern to researchers due to the effects on statistical procedures such as measures of central tendency and dispersion. Robust methods were motivated by nonnormal distributions where outliers can be assumed to have contaminated the model, and are methods that are not affected by small deviations from normality. The trimmed mean (X¯t) is an example of a robust method, and is a robust estimator of the population mean that can be used when the underlying distribution of the data is normal. When working with the trimmed mean (X¯t), one may want to determine how accurately the sample trimmed mean estimates the population mean by forming a bracketed interval around the sample trimmed mean. In forming a bracketed interval around X¯t, the sample winsorized standard deviation (sw) is commonly used as a robust measure of dispersion. This study investigated alternatives to sw in forming a bracketed interval around the sample trimmed mean. A Monte Carlo study was used to evaluate six alternative measures of dispersion on ten distributions with an underlying symmetric structure using both a 2 x 10% and 2 x 20% symmetric trim. Resulting bracketed interval coverage and widths were compared to the performance of sw. The results of this study support the use of sw in calculating bracketed intervals around the sample trimmed mean. S w was the only measure of dispersion with robust coverage rates across all distributions, alpha levels, and trim percentages tested. Generally bracketed interval widths were shorter for sw. One measure of dispersion (Srecode1, a combination of trimming and winsorizing) resulted in shorter bracketed intervals using a 2 x 20% trim. However, coverage was robust for only 70% of the distributions tested. In general, the results of this study support light vs. heavy trimming.
Bunner, Jennifer M., "Forming a bracketed interval around the trimmed mean : alternatives to S[subscript w]" (2003). Wayne State University Dissertations. 3312.