The robustness of confidence intervals for effect size in one way designs with respect to departures from normality
Master of Science === Department of Statistics === Paul Nelson === Effect size is a concept that was developed to bridge the gap between practical and statistical significance. In the context of completely randomized one way designs, the setting considered here, inference for effect size has only be...
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ndltd-KSU-oai-krex.k-state.edu-2097-136762017-03-03T15:44:41Z The robustness of confidence intervals for effect size in one way designs with respect to departures from normality Hembree, David Effect size Robustness Confidence interval Statistics (0463) Master of Science Department of Statistics Paul Nelson Effect size is a concept that was developed to bridge the gap between practical and statistical significance. In the context of completely randomized one way designs, the setting considered here, inference for effect size has only been developed under normality. This report is a simulation study investigating the robustness of nominal 0.95 confidence intervals for effect size with respect to departures from normality in terms of their coverage rates and lengths. In addition to the normal distribution, data are generated from four non-normal distributions: logistic, double exponential, extreme value, and uniform. The report discovers that the coverage rates of the logistic, double exponential, and extreme value distributions drop as effect size increases, while, as expected, the coverage rate of the normal distribution remains very steady at 0.95. In an interesting turn of events, the uniform distribution produced higher than 0.95 coverage rates, which increased with effect size. Overall, in the scope of the settings considered, normal theory confidence intervals for effect size are robust for small effect size and not robust for large effect size. Since the magnitude of effect size is typically not known, researchers are advised to investigate the assumption of normality before constructing normal theory confidence intervals for effect size. 2012-04-26T18:38:33Z 2012-04-26T18:38:33Z 2012-04-26 2012 May Report http://hdl.handle.net/2097/13676 en_US Kansas State University |
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Effect size Robustness Confidence interval Statistics (0463) |
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Effect size Robustness Confidence interval Statistics (0463) Hembree, David The robustness of confidence intervals for effect size in one way designs with respect to departures from normality |
description |
Master of Science === Department of Statistics === Paul Nelson === Effect size is a concept that was developed to bridge the gap between practical and statistical significance. In the context of completely randomized one way designs, the setting considered here, inference for effect size has only been developed under normality. This report is a simulation study investigating the robustness of nominal 0.95 confidence intervals for effect size with respect to departures from normality in terms of their coverage rates and lengths. In addition to the normal distribution, data are generated from four non-normal distributions: logistic, double exponential, extreme value, and uniform.
The report discovers that the coverage rates of the logistic, double exponential, and
extreme value distributions drop as effect size increases, while, as expected, the coverage rate of the normal distribution remains very steady at 0.95. In an interesting turn of events, the uniform
distribution produced higher than 0.95 coverage rates, which increased with effect size. Overall, in the scope of the settings considered, normal theory confidence intervals for effect size are robust for small effect size and not robust for large effect size. Since the magnitude of effect size is typically not known, researchers are advised to investigate the assumption of normality before constructing normal theory confidence intervals for effect size. |
author |
Hembree, David |
author_facet |
Hembree, David |
author_sort |
Hembree, David |
title |
The robustness of confidence intervals for effect size in one way designs with respect to departures from normality |
title_short |
The robustness of confidence intervals for effect size in one way designs with respect to departures from normality |
title_full |
The robustness of confidence intervals for effect size in one way designs with respect to departures from normality |
title_fullStr |
The robustness of confidence intervals for effect size in one way designs with respect to departures from normality |
title_full_unstemmed |
The robustness of confidence intervals for effect size in one way designs with respect to departures from normality |
title_sort |
robustness of confidence intervals for effect size in one way designs with respect to departures from normality |
publisher |
Kansas State University |
publishDate |
2012 |
url |
http://hdl.handle.net/2097/13676 |
work_keys_str_mv |
AT hembreedavid therobustnessofconfidenceintervalsforeffectsizeinonewaydesignswithrespecttodeparturesfromnormality AT hembreedavid robustnessofconfidenceintervalsforeffectsizeinonewaydesignswithrespecttodeparturesfromnormality |
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1718418395312947200 |