First, the country-level analyses presented by OD and HBW violate the assumption of independent sampling (i.e., the statistical assumption of independence of errors) as countries are geographically (and historically) clustered (Ross and Homer, 1976; Pollet et al., 2014). This is also known as “Galton's problem.” Countries from the same region have undergone a similar development and cannot be considered independent data points. As a consequence, all significance tests are biased (Kruskal, 1988). This applies to OD, HBW, and many other nation-level analyses. We illustrate the consequences of Galton's problem with data from HBW. HBW presented results showing that country age was positively related with the Environmental Performance Index (EPI). The EPI consists of the subscales Environmental Health (EH) and Ecosystem Vitality (EV); Figure Figure11 clearly shows that the scores cluster by region.
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机译：首先，OD和HBW提出的国家级分析违反了独立采样的假设（即误差独立性的统计假设），因为国家在地理上（和历史上）是聚类的（Ross and Homer，1976; Pollet等， 2014）。这也称为“加尔顿问题”。来自同一地区的国家也经历了类似的发展，因此不能视为独立的数据点。结果，所有显着性检验都是有偏见的（Kruskal，1988）。这适用于OD，HBW和许多其他国家级别的分析。我们用HBW的数据说明了高尔顿问题的后果。 HBW提供的结果表明，国家年龄与环境绩效指数（EPI）呈正相关。 EPI包括环境健康（EH）和生态系统活力（EV）子量表;图图11清楚地显示了分数按区域聚类。
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