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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