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• W1976548629 abstract "An F statistic was proposed by Good and Chernick (1993 Good , P. I. , Chernick , M. ( 1993 ). Testing the equality of variances of two populations. Unpublished manuscript . [Google Scholar]) in an unpublished paper, to test the hypothesis of the equality of variances from two independent groups using the bootstrap; see Hall and Padmanabhan (1997 Hall , P. , Padmanabhan , A. R. ( 1997 ). Adaptive inference for the two sample problem . Technometrics 39 : 412 – 422 .[Taylor & Francis Online] , [Google Scholar]), for a published reference where Good and Chernick (1993 Good , P. I. , Chernick , M. ( 1993 ). Testing the equality of variances of two populations. Unpublished manuscript . [Google Scholar]) is discussed. We look at various forms of bootstrap tests that use the F statistic to see whether any or all of them maintain the nominal size of the test over a variety of population distributions when the sample size is small. Chernick and LaBudde (2010 Chernick , M. R. , LaBudde , R. A. ( 2010 ). Revisiting qualms about bootstrap confidence intervals . American Journal of Mathematical and Management Sciences 29 : 437 – 456 .[Taylor & Francis Online] , [Google Scholar]) and Schenker (1985 Schenker , N. ( 1985 ). Qualms about bootstrap confidence intervals . Journal of the American Statistical Association 80 : 360 – 361 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) showed that bootstrap confidence intervals for variances tend to provide considerably less coverage than their theoretical asymptotic coverage for skewed population distributions such as a chi-squared with 10 degrees of freedom or less or a log-normal distribution. The same difficulties may be also be expected when looking at the ratio of two variances. Since bootstrap tests are related to constructing confidence intervals for the ratio of variances, we simulated the performance of these tests when the population distributions are gamma(2,3), uniform(0,1), Student's t distribution with 10 degrees of freedom (df), normal(0,1), and log-normal(0,1) similar to those used in Chernick and LaBudde (2010 Chernick , M. R. , LaBudde , R. A. ( 2010 ). Revisiting qualms about bootstrap confidence intervals . American Journal of Mathematical and Management Sciences 29 : 437 – 456 .[Taylor & Francis Online] , [Google Scholar]). We find, surprisingly, that the results for the size of the tests are valid (reasonably close to the asymptotic value) for all the various bootstrap tests. Hence we also conducted a power comparison, and we find that bootstrap tests appear to have reasonable power for testing equivalence of variances." @default.
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• W1976548629 date "2011-10-24" @default.
• W1976548629 modified "2023-09-26" @default.
• W1976548629 title "A Bootstrap Test for Comparing Two Variances: Simulation of Size and Power in Small Samples" @default.
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• W1976548629 doi "https://doi.org/10.1080/10543406.2011.611082" @default.
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