Vol. 19 No. 1 January/February 2008 articles 4 I n this article, we present a brief over- view of some of our recent work on the quantitative breakdown of all sampling and analytical errors in determination of protein content in bulk wheat using single- seed or single-kernel near infrared (SKNIR) spectroscopy. 1 SKNIR has facilitated a total breakdown of error contributions generated by the sampling processes as far as the fundamental sampling error (FSE) and the grouping and segregation error (GSE) which are usually only theoretical abstractions. 2–6 Theory of sampling (TOS) Most often an analytical result, be it a destructive standard analysis or a non- destructive NIR spectrum, is a property estimate measured on an analytical volume considerably smaller than the volume of the lot (L) being characterised. The inevitable estimation errors generated during the mass reduction process, together with analysis, are substantiated by Pierre Gy’s Theory of Sampling (TOS), 2–6 while realising that the true value or spectrum remains unknown. With reference to the fundamental sampling principle, it is possible to extract unbiased analytical volumes for materials comprised of discrete fragments, e.g. powders, grains or soil. Such materials are by definition zero-dimensional (0D) as all parts of the lot are equally accessible: from a practical point of view, it is thus mechanically pos- sible to extract truly representative analyti- cal volumes by ensuring that all parts of the material have an equal probability of ending up in the sample cup used. The sampling process The fact that the sampling processes may cause unrealistic variance estimates and biased results is often ignored, at least when measuring properties of apparently uniform particulate materials. This could have pronounced effects on assessing the quality of the materials investigated. In envi- ronmental studies, poor sampling leading to completely random results is sometimes referred to as “the casino effect”. 7 Sampling protocols involving riffle splitters, rotational dividers, coning-and-quartering, alternate shovelling, incremental sampling and simple grab sampling for mass reduc- tion of particulate materials have already been thoroughly investigated. 8–11 These studies, however, involved only mixtures of inert, pure materials. The samples derived were separable by sieving, 8,11 dissolution 9–10 and magnetism 9 and their relative compo- sitions could conveniently be assessed in relation to the known composition. All inves- tigations concluded that the heterogeneity of the lot was only translated satisfactorily into the analytical volume by using static rif- fle splitters or their dynamic equivalents, the rotational dividers, preferably with a large number of chutes (rotations). Shovelling, coning-and-quartering and grab sampling techniques all failed by returning biased composition estimates, large replication variances and loss of material. Our TOS investigation of the protein con- tent in wheat 1 was based on field wheat lots composed of composite complex fragments, i.e. wheat kernels. Original lots weighed 2631–4686 g. We compared representa- tive riffle splitting with non-representative grab sampling to reach the analytical vol- ume of 42 seeds which totalled 1.66–2.02 g on average; this corresponded to sampling rates of from 1 : 2324 to 1 : 1566. Using NIR transmission spectroscopy (850–1050 nm), we were able to assess the quality of each individual kernel. 12 This was particularly interesting as this made it possible to quan- tify not only the total variance but also break it down into its major components, and bias, induced by grab sampling. The sampling errors according to TOS The global estimation error (GEE ), i.e. the difference between the true grade of the lot ( a L ) and the analytical result ( a R ), can be Single-kernel near infrared analysis of bulk wheat heterogeneity—a theory of sampling reference study 1 Erik Tønning, a Lars Nørgaard, b Søren B. Engelsen, b Lene Pedersen c and Kim H. Esbensen d a Department of Food Science, Faculty of Agricultural Sciences, University of Aarhus, DK-5792 Aarslev, Denmark. E-mail: erik.tonning@agrsci.dk b Department of Food Science, Faculty of Life Sciences, University of Copenhagen, DK-1958 Frederiksberg C, Denmark. E-mail: lan@life.ku.dk, se@life.ku.dk c Department of Chemical Engineering, Faculty of Engineering, University of Southern Denmark, DK-5230 Odense M, Denmark. E-mail: lp@kbm.sdu.dk d ACABS, Aalborg University Esbjerg, DK-6700 Esbjerg, Denmark. E-mail: kes@aaue.dk doi: 10.1255/nirn.1057 “SKNIR technology... will have a huge potential for heterogeneity characterisation and for large and small scale sorting according to internal complex quality traits and for breeding purposes”