Compositional statistical analysis of soil 31P-NMR forms

• Soil 31P-NMR forms are compositional data.
• Ordinary log transformation generated statistically erroneous results depending on measurement scale.
• Compositional analysis using clr and ilr transformations avoided statistical analysis biases.

Phosphorus (P) forms determined by 31P nuclear magnetic resonance spectroscopy (31P-NMR) are compositional data (i.e., parts of some whole bounded between 0 and the unit of measurement). Because compositional data are intrinsically related to each other within a closed pre-defined compositional space, a simple log transformation, variable by variable, or any other transformation of the compositional variables may produce statistically erroneous results. However, most studies analyze the P forms as single components rather than parts of some whole such as total P (TP) or soil dry mass, leading systematically to methodological biases and conflicting interpretations. Compositional data analysis using centered log-ratio (clr) or isometric log-ratio (ilr) coordinates avoids such difficulties and preserves sub-compositional coherence in the analysis. The objective of this study was to compare classical and compositional methods for the statistical analysis of 31P-NMR P data expressed as proportions of TP or concentrations relative to soil dry mass. Two published datasets were used. Analyses of variance and regression analysis with soil pH were conducted on P species percentages scaled on TP or as untransformed concentrations scaled on a soil dry-weight basis as well as their ordinary log, centered log-ratios (clr) and isometric log-ratios (ilr). Contradictory F-statistics values and coefficients of correlation with soil pH were obtained for the untransformed and ordinary log transformed 31P-NMR P data expressed as proportions or concentrations. In contrast, statistical results were the same regardless of the measurement unit when P compound percentages were clr-transformed. Using orthogonal ilr coordinates, 31P-NMR P data were correlated to soil properties and to each other and synthesized into a multivariate distance without methodological bias. We conclude that the variance and regression analyses of molecular P species are scale-dependent and that the clr- and the ilr-transformations should be used to unbiasedly analyze the P fractions and avoid conflicting interpretations.

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