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首页> 外文期刊>The Science of the Total Environment >The bivariate statistical analysis of environmental (compositional) data
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The bivariate statistical analysis of environmental (compositional) data

机译：环境（组成）数据的二元统计分析

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摘要

Environmental sciences usually deal with compositional (closed) data. Whenever the concentration of chemical elements is measured, the data will be closed, i.e. the relevant information is contained in the ratios between the variables rather than in the data values reported for the variables. Data closure has severe consequences for statistical data analysis. Most classical statistical methods are based on the usual Euclidean geometry — compositional data, however, do not plot into Euclidean space because they have their own geometry which is not linear but curved in the Euclidean sense. This has severe consequences for bivariate statistical analysis: correlation coefficients computed in the traditional way are likely to be misleading, and the information contained in scatterplots must be used and interpreted differently from sets of non-compositional data. As a solution, the ilr transformation applied to a variable pair can be used to display the relationship and to compute a measure of stability. This paper discusses how this measure is related to the usual correlation coefficient and how it can be used and interpreted. Moreover, recommendations are provided for how the scatterplot can still be used, and which alternatives exist for displaying the relationship between two variables.
机译：环境科学通常处理成分（封闭）数据。每当测量化学元素的浓度时，数据将被关闭，即相关信息包含在变量之间的比率中，而不是包含在为变量报告的数据值中。数据关闭会对统计数据分析产生严重后果。大多数经典的统计方法都基于通常的欧几里得几何体-成分数据不会绘制到欧几里得空间中，因为它们具有自己的几何形状，该几何形状不是线性而是在欧几里得意义上是弯曲的。这会对双变量统计分析产生严重后果：以传统方式计算的相关系数可能会产生误导，并且散点图中包含的信息的使用和解释必须与非组合数据集不同。作为解决方案，应用于变量对的ilr变换可用于显示关系并计算稳定性的度量。本文讨论了该度量如何与通常的相关系数相关以及如何使用和解释它。此外，还提供了有关如何仍可使用散点图以及存在哪些替代方案来显示两个变量之间关系的建议。

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