"Today it seems impossible to introduce students in any significant way to all of the apparatus and instruments available for separation and measurement. Anyway, I know of no evidence that industry wants the product of a button-pushing, meter-reading excursion past an array of expensive instruments." So stated M.G. Mellon of Purdue University at a meeting in 1959 (1), describing the goals of a university course in quantitative analysis. Mellon went on to say that "It seems obvious that analyses cannot be made without samples [and for sample selection and preparation], homogeneous materials present no problem, provided enough is available for the required determination(s). In contrast, obtaining a representative sample from some heterogeneous materials is one of the most difficult analytical operations. In spite of this fact, a recent survey of 50 books revealed that 20% of them did not mention sampling." In 1971, Herb Laitinen, Editor of Analytical Chemistry, also wrote about the full role of the analytical chemist in the experimental design for sampling as well as in the measurement and interpretation of data (2).

Kenneth L. Busch

In 2009, it might seem even more impossible to create an analytical chemistry curriculum that balances breadth of coverage with depth of education, as the tools for separation and measurement are far more numerous and diverse than in 1959. Attaining a balance is made even more difficult by the fact that the time allotted to an undergraduate university education remains about the same, and the fact that educational technology sometimes leads to information overload rather than enhanced understanding. It is safe to assume, however, that industry probably still prefers chemists who understand the basics of analysis, rather than those who might simply be button-pushers. Understanding the basics may be one of the reasons this column has appeared since 1995, and why continuing education in all of analytical chemistry has expanded within professional societies and other venues. Suggestions for incorporating sampling theory in undergraduate curriculum have been discussed (3) (using as an example the determination of metals in breakfast cereals with inductively coupled plasma spectroscopy), and specialized texts are available (4–6).

Every new advance in instrumentation alters our understanding of the components that comprise a sample and reflects on measures that must be used to determine whether a sampling protocol is valid. With new analytical measurement capabilities, samples previously thought to be homogeneous may be found to exhibit significant heterogeneity. The heterogeneity may be a spatial or time distribution of sample components. A rational evaluation of sampling has always embraced these possibilities. In the final analysis, even large volume and well-mixed samples can only be defined as uniform or not when the component to be measured is specified and its distribution determined. It is prudent at the beginning of an analysis to assume that a sample volume is heterogeneous for all samples. Then, as the measurement proceeds, a limit can be established for each component at which variation will be deemed significant. Therefore, an accurate characterization of the sampling volume can only occur after the scouting data are acquired and evaluated.

Although more sophisticated theories of sampling have been developed, and these are now supported by more robust statistical tools, proper sampling is as difficult now as it was in 1959. Proper sampling still requires careful experimental design and the devotion of considerable time and resources from the analyst. The study of sampling melds mathematics, mechanics, and chemistry, and it probably still does not receive the attention it merits in general texts of analytical chemistry. In books that are written specifically for mass spectrometry, sampling is usually not mentioned at all, yielding its space to descriptions of instrumentation and details of spectral interpretation. One is left to wonder how much of the recorded mass spectrometry (MS) data may be both accurate and precise, but ultimately not suited to answer the question at hand. Challenges in sampling for MS have become especially evident as portable mass spectrometers have been taken into the field, and the analyst is faced with real-time sampling decisions. Similarly, mass spectrometers are now incorporated into production lines as quality control measurement (as in brewing), and samples may be presegmented as discrete units, or even configured as their final forms (such as a pill for which the level of active ingredient is to be assayed).

In this column, some of the basic considerations for valid sampling are described, with some examples pertinent to MS. A later column will drill down to more specific situations, such as sampling for in-field analysis or process control sampling.

We begin with an overview of basic sampling strategies for populations of samples. These strategies have been described as: random sampling, stratified random sampling, systematic sampling, and rational subgrouping. Each strategy has its particular applications area, and the selection depends upon the character of the population itself as well as the type of study (population or process) to be conducted — that is, what is to be measured. In general, a population study seeks to establish the characteristics or components of a population when they are not expected to change over time. A process study follows changes in an evolving population.

A key characteristic of random sampling is that each unit or subset of the population has an equal chance of being selected as the sample for measurement. Just as logically, random sampling only works when there is no evident stratification, segregation, or bias. The fact that bias is unknown cannot be viewed as justification for random sampling. Measures taken to reduce sample nonhomogeneity and remove bias include dissolution, stirring, mixing, or grinding.