Calibration of compositional measurements

ABSTRACT

The aim of calibration is usually to express a linear relationship between errorless measurements obtained by two methods (or, alternatively, by two measuring devices). When the measurement results are compositional data, i.e., multivariate observations carrying only relative information (proportions, percentages), a special treatment is necessary. In this article, an analogy between the compositional variation array and the matrices of the predicted values and residual variances from univariate calibrations is derived, which is useful for descriptive statistics. Consequently, tests for verification of conformity between two methods of measurement are proposed. Theoretical results are applied to an example from biochemistry.

KEYWORDS:

• Log-ratio transformations
• Compositional variation array
• Calibration line
• Multiple comparisons

Mathematics Subject Classification:

• Primary 62J05
• Secondary 62F03