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A bootstrap test for comparing two variances: simulation of size and power in small samples
Jiajing Sun1, Michael R Chernick, Robert A LaBudde
1Economics Research Group Management School, University of Liverpool, Liverpool, United Kingdom. sunjiajing@hotmail.com
Journal of Biopharmaceutical Statistics
|October 26, 2011
Summary
This study surprisingly found that bootstrap tests using the F statistic maintain accurate test sizes for comparing variances across various distributions, even with small sample sizes. These bootstrap methods also demonstrate reasonable power for testing variance equivalence.
Area of Science:
- Statistics
- Statistical Inference
- Computational Statistics
Background:
- The F statistic, proposed by Good and Chernick (1993), is used for testing the equality of variances between two independent groups via bootstrapping.
- Previous research indicated that bootstrap confidence intervals for variances exhibit reduced coverage for skewed distributions (e.g., chi-squared, log-normal).
- Similar issues were anticipated for tests involving the ratio of variances, a common application of the F statistic in bootstrapping.
Purpose of the Study:
- To evaluate the performance of various bootstrap tests employing the F statistic.
- To determine if these tests maintain nominal size across diverse population distributions with small sample sizes.
- To assess the power of bootstrap tests for detecting differences in variances.
Main Methods:
- Simulated the performance of bootstrap F statistic tests for variance equality.
- Utilized various population distributions: gamma(2,3), uniform(0,1), Student's t (10 df), normal(0,1), and log-normal(0,1).
- Compared test sizes against asymptotic values and conducted power comparisons.
Main Results:
- Surprisingly, all tested bootstrap F statistic methods maintained valid test sizes, closely approximating asymptotic values across all simulated distributions.
- The bootstrap tests demonstrated reasonable power in detecting differences when testing for variance equivalence.
- Results were consistent despite known issues with bootstrap confidence intervals for skewed distributions.
Conclusions:
- Bootstrap tests utilizing the F statistic are robust in maintaining nominal size, even for non-normal and skewed distributions with small sample sizes.
- These methods offer a viable and powerful approach for testing the equality of variances between two independent groups.
- The findings challenge prior expectations regarding bootstrap performance with skewed data for variance ratio tests.
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