Protein heterogeneity in wheat lots using single-seed NIT — A Theory of Sampling (TOS) breakdown of all sampling and analytical errors

An in-depth heterogeneity analysis of wheat lots from varying field experiments with respect to protein concentration was conducted in order to quantify and compare both sampling and analytical errors as defined by the Theory of Sampling (TOS). Thirty wheat samples of forty-two seeds were extracted from three different wheat lots. Half of these were extracted using a non-optimal spoon (grab sampling) and the other half were extracted using a riffle splitter. Ten additional samples of forty-two seeds were extracted using a riffle splitter from ten different wheat lots. The protein content of every single-seed was determined by Near-Infrared Transmission (NIT) spectroscopy based on a multivariate calibration to Kjeldahl with Partial Least Squares Regression (PLS-R). The effect of orientation and number of replicate measurements of the individual seeds in the NIT beam was investigated for minimizing the analytical error as well the resulting time requirements. Remarkably, the best prediction model with respect to Root Mean Squared Error of Cross Validation (RMSECV) was obtained by only recording three replicate NIT spectra of the seeds in only one specific orientation. The variance of the Global Estimation Error (GEE) of both the riffle splitter and the spoon sampling processes was estimated as well as its components, the Fundamental Sampling Error (FSE), the Grouping and Segregation Error (GSE), the Incorrect Sampling Errors (ISE) and the Total Analytical Error (TAE). The bias induced by non-probabilistic spoon extraction was also estimated. The GEE variance of the spoon extractions was seventy percent higher than that of the riffle split samples. The sampling variances of FSE, GSE and ISE were all of the same order of magnitude, each approximately ten times higher than the TAE variance. The squared bias of the spoon sampling was approximately twice the magnitude of the sampling variances and thus contributed significantly to the representativity score. Spoon sampling representativity was three times the size of that for the riffle splitter. Order of magnitude estimates of the Constitutional Heterogeneity (CHL) as well as the Distributional Heterogeneity (DHL) for a forty-two seed riffle split sample was derived. In this investigation the fundamental concepts of TOS have been investigated and estimates of all sampling and analytical errors have been presented for a specific zero-dimensional composite material. The ability of TOS for quantifying and evaluatin