Bootstrap hypothesis testing for some common statistical problems: A critical evaluation of size and power properties |
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| Affiliation: | 1. Department of Physics, University of Helsinki, P.O. Box 64, FI-00014 Helsinki, Finland;2. Instituto de Física Teórica (IFT/UNESP), UNESP - São Paulo State University, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II Barra Funda, CEP 01140-070 São Paulo, SP, Brazil;1. Department of Methodology and Statistics, Tilburg University, Tilburg, The Netherlands;2. Department of Psychology, University of Amsterdam, Amsterdam, The Netherlands;1. Banner Alzheimer''s Institute, Phoenix, AZ, USA;2. Arizona Alzheimer''s Consortium, Phoenix, AZ, USA;3. Pentara Corporation, Salt Lake City, UT, USA;4. Department of Mathematics and Statistics, Arizona State University, Tempe, AZ, USA;5. Rush Alzheimer''s Disease Center, Rush University Medical Center, Chicago, IL, USA;6. Department of Family Medicine, Rush University Medical Center, Chicago, IL, USA;7. Department of Neurological Sciences, Rush University Medical Center, Chicago, IL, USA;8. Department of Behavioral Sciences, Rush University Medical Center, Chicago, IL, USA;9. Department of Psychiatry, University of Arizona, Tucson, AZ, USA;10. Neurogenomics Division, Translational Genomics Research Institute, Phoenix, AZ, USA |
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| Abstract: | The construction of bootstrap hypothesis tests can differ from that of bootstrap confidence intervals because of the need to generate the bootstrap distribution of test statistics under a specific null hypothesis. Similarly, bootstrap power calculations rely on resampling being carried out under specific alternatives. We describe and develop null and alternative resampling schemes for common scenarios, constructing bootstrap tests for the correlation coefficient, variance, and regression/ANOVA models. Bootstrap power calculations for these scenarios are described. In some cases, null-resampling bootstrap tests are equivalent to tests based on appropriately constructed bootstrap confidence intervals. In other cases, particularly those for which simple percentile-method bootstrap intervals are in routine use such as the correlation coefficient, null-resampling tests differ from interval-based tests. We critically assess the performance of bootstrap tests, examining size and power properties of the tests numerically using both real and simulated data. Where they differ from tests based on bootstrap confidence intervals, null-resampling tests have reasonable size properties, outperforming tests based on bootstrapping without regard to the null hypothesis. The bootstrap tests also have reasonable power properties. |
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