Department of Plant and Environmental Sciences, University of Gothenburg, Box 461, 40530 Gothenburg, Sweden.
J Environ Manage. 2011 Mar;92(3):610-9. doi: 10.1016/j.jenvman.2010.09.026. Epub 2010 Oct 28.
Field surveys of biological responses can provide valuable information about environmental status and anthropogenic stress. However, it is quite usual for biological variables to differ between sites or change between two periods of time also in the absence of an impact. This means that there is an obvious risk that natural variation will be interpreted as environmental impact, or that relevant effects will be missed due to insufficient statistical power. Furthermore, statistical methods tend to focus on the risks for Type-I error, i.e. false positives. For environmental management, the risk for false negatives is (at least) equally important. The aim of the present study was to investigate how the probabilities for false positives and negatives are affected by experimental set up (number of reference sites and samples per site), decision criteria (statistical method and α-level) and effect size. A model was constructed to simulate data from multiple reference sites, a negative control and a positive control. The negative control was taken from the same distribution as the reference sites and the positive control was just outside the normal range. Using the model, the probabilities to get false positives and false negatives were calculated when a conventional statistical test, based on a null hypothesis of no difference, was used along with alternative tests that were based on the normal range of natural variation. Here, it is tested if an investigated site is significantly inside (equivalence test) and significantly outside (interval test) the normal range. Furthermore, it was tested how the risks for false positives and false negatives are affected by changes in α-level and effect size. The results of the present study show that the strategy that best balances the risks between false positives and false negatives is to use the equivalence test. Besides tests with tabulated p-values, estimates generated using a bootstrap routine were included in the present study. The simulations showed that the probability for management errors was smaller for the bootstrap compared to the traditional test and the interval test.
野外生物响应调查可为环境状况和人为压力提供有价值的信息。然而，即使在没有影响的情况下，生物变量在不同地点之间也会有所不同，或者在两个时间段之间发生变化。这意味着存在明显的风险，即自然变异将被解释为环境影响，或者由于统计能力不足而错过相关影响。此外，统计方法往往侧重于第一类错误（即假阳性）的风险。对于环境管理，假阴性的风险（至少）同样重要。本研究的目的是调查实验设置（参考地点数量和每个地点的样本数量）、决策标准（统计方法和α水平）和效应大小如何影响假阳性和假阴性的概率。构建了一个模型来模拟来自多个参考地点、阴性对照和阳性对照的数据。阴性对照取自与参考地点相同的分布，阳性对照则刚好超出正常范围。使用该模型，当使用基于无差异零假设的传统统计检验以及基于自然变异正常范围的替代检验时，计算得到假阳性和假阴性的概率。在这里，检验调查地点是否明显在正常范围之内（等效性检验）和明显在正常范围之外（区间检验）。此外，还测试了α水平和效应大小变化如何影响假阳性和假阴性的风险。本研究的结果表明，在假阳性和假阴性风险之间取得最佳平衡的策略是使用等效性检验。除了具有表列 p 值的检验外，本研究还包括使用自举程序生成的估计值。模拟表明，与传统检验和区间检验相比，自举检验的管理错误概率更小。
