Abstract

The Extended Bootstrap (EB) assessment approach was developed for the examination of relationships of Type I error, power, sample size (n), and effect size (ES) for statistical tests of ecological data. The EB approach was applied to univariate and multivariate statistical analyses of a large data set collected from an ongoing, multiple stressor bioassessment study of watersheds in the Central Valley, San Francisco, and Central Coast areas of California. Benthic metrics were created that either increased or decreased monotonically with stress (toxicants or metrics indicative of habitat quality). Type I errors were stable for all statistical tests that were evaluated. The relationships between n and ES displayed patterns of “diminishing returns” for all statistical tests: i.e. an increasingly larger n was required to detect decreasingly smaller ES. Nonetheless, the n’s collected across the watersheds and within a selected watershed were sufficient to detect even small correlations between representative benthic metrics and potential stressors with high power. The power and robustness of a novel method using EB and previously described statistical techniques designed to address multicollinearity were shown to approach those of simpler univariate regressions. Potential applications of the EB approach for experimental design, data assessment and interpretation, and hypothesis testing are discussed.

摘要

开发了扩展引导程序（EB）评估方法，用于检查I型误差，功效，样本量（n）和效应量（ES）之间的关系，以进行生态数据的统计测试。EB方法应用于从正在进行的，多压力源生物评估研究中对加利福尼亚中央谷地，旧金山和加利福尼亚中部海岸地区的流域进行的大型数据集的单变量和多变量统计分析。创建的底栖指标随压力单调增加或减少（有毒物质或指示栖息地质量的指标）。对于所有评估的统计测试，I型错误都是稳定的。n之间的关系ES显示所有统计检验的“收益递减”模式：即，检测到越来越小的ES需要增加n。尽管如此，在整个分水岭和选定分水岭内收集的n足以检测代表性底栖指标与高功率潜在压力源之间的很小关联。结果表明，使用EB的新方法的强大功能和稳健性以及先前描述的旨在解决多重共线性的统计技术可以逼近简单的单变量回归。讨论了EB方法在实验设计，数据评估和解释以及假设检验中的潜在应用。