Univariate statistical analysis of environmental (compositional) data: problems and possibilities.

Area of Science:

• Environmental Science
• Geochemistry
• Data Science

Background:

• Compositional data, prevalent in environmental science, represent parts of a whole and inherently sum to a constant (e.g., 100 wt.%).
• The 'closure' property of compositional data is often overlooked, even when only a subset of components is measured.
• Classical statistical methods and transformations are ill-suited for analyzing compositional data due to its inherent constraints.

Purpose of the Study:

• To investigate the impact of data closure on basic univariate statistical analyses.
• To demonstrate the necessity of overcoming data closure before applying standard statistical measures.
• To highlight the limitations of classical statistical techniques when applied to compositional datasets.

Main Methods:

• Analysis of the univariate case of compositional data.
• Demonstration of how data closure affects fundamental statistical measures (mean, standard deviation).
• Evaluation of the consequences for statistical tests reliant on variance.

Main Results:

• Standard statistical measures like mean and standard deviation are mathematically inappropriate for closed compositional data.
• Data closure must be addressed prior to calculating descriptive statistics or creating data distribution plots (e.g., histograms).
• Statistical tests based on standard deviation or variance produce erroneous results when applied to raw compositional data.

Conclusions:

• Classical statistical methods are fundamentally flawed when applied directly to compositional data.
• Specialized methods are required to correctly analyze compositional data, particularly in environmental science applications.
• Ignoring data closure leads to statistically invalid conclusions and unreliable scientific findings.