Understanding How Analytical Tests Are Selected Michael Guarnieri Department of Pharmacology, Johns Hopkins University School of Medicine, 725 N. Wolfe Street, Baltimore, MD 21205
Chemists sometimes are asked to describe their work to nonscientists. The responsibility for this task is growing, especially in the areas of forensics, clinical toxicology, and hazardous wastes. The audience is not always friendly; a t times, it may be hostile. In some public hearings, for example, highly educated people will try to confuse the presentation of any data that do not support their objectives. In such situations, chemists not only must describe results, they must explain them. One of the most difficult questions is how do chemists analyze unknowns? I t would be easy to testify that unknowns are identified through an orderly series of tests that are based on chemical categories. According to this argument, materials can be classified as organic or inorganic. If the unknown is inorganic, it is a metal or a nonmetal. If i t is a nonmetal, i t is tested for this or that type of ion, and so on. Although this is easy testimony, i t potentially is misleading, and it can become a trap. The scenario assumes the chemist can get enough of the unknown to conduct an exhaustive series of tests. This is rarely the case in forensic work, and never the case in clinical studies. Chemists almost never analyze something for everything. From a practical view, nobody could afford the costs for such analyses. Chemists make choices. How else could one identify the infinite variety of analytes present in the infinite variety of matrices? Despite arguments that analyses are guided by time-tested scientific principles, choices-meaning, the selection of tests-are the rule rather than the exception in forensics, clinical studies, and waste analyses. Unless the chemist clearly recognizes and understands how tests are selected, a hostile examiner can claim the "rational selection" of tests is nothing more than "irrational bias", or worse. In a public hearing, and in a courtroom, such a claim can destroy even expert witnesses. I t is well recognized that chemists frequently face difficult decisions when organizing data from chemical analyses. Rogers recently described the special challenges encountered when the detection limit of a compound is close to its regulatory limits ( I ) . On the other hand, the selection (rational or irrational) of tests for unknowns is so common and i t operates on so many intellectual levels that much of the work is done without recognition, even by experienced chemists. Sometimes, chemists will provide a clear outline of their reasoning for an analytical procedure. Rarely do they attempt to define a mental process that gave rise to the outline. I t is not surprising, therefore, that there is little or no literature on the intellectual processes, the logic, that chemists use to analyze unknown substances. The lack of study is of concern because of the increasing likelihood chemists will he required to explain and defend the diagnostic logic used to analyze unknowns. The purpose of this paper is to suggest there is a common and general process by which analytical decisions are made. The understanding of this process should be a primary objective in teaching analytical chemistry. I t is important, therefore, to present a logical and instructive examination of the pertinent reasoning involved in selecting the strategy for unknown analyses.
Methods I t seems reasonable to postulate that chemists select tests hased on probabilities. These probabilities are derived from a series of measurements hased on exhaustive chemical categories, as described above. For example, the probability an unknown is inorganic ranges from 1(absolute certainty) too. This argument claims that each choice is hased on the examination of different alternatives. The choices, therefore, are logical, and there is no bias. The chemist arrives a t his or her conclusion via an organized selection process in exactly the same fashion a computer would use. At first glance, this seems to hea compelfing argument. I t requires fuither investigation.
A Mathematical Approach Ideallv. to select the most heloful analvsis. the chemist needs td calculate and compare ihe prohabiliiies of various chemicals that could give an unknown material its characteristics. An odorlesswhite powder is unlikely to contain significant amounts of ethyl ether because et her has a strung odor and is quite volatile. The probnhiliries, therefore, indude what a material could and could not he. The menral strategies a chemist uses to solve the analytical calculation can he expressed in probahility terms as follows: The probability P that a chemical or mixture gives an unknown a specific set of characteristics is written as P(chemical)g(materialcharacteristics) where g means "given". To select the most likely analysis, the chemist must estimate this orobabilitv for all the oossible chemicals, taking into accbunt all [he charactehics present in the case. The most direct wav to do all this is with kayes's formula (Z),which in its simpl&t form can he written
The difficulty of the analytical task can be appreciated by considerine each art of this formula. Prchrmicoi~glcharocterislira).The chemist tries to estimate the orohabilitv that a material conrains certain rhemicals hased on the characteristics of the suhstance and other information. Chemical knowledge, however, is not usually collected, reported, or learned in this form. Rather, chemists learn the characteristics that occur with each chemical or mixrure ( 3 ) .Most of the literature is organized according to chemicals. The analyst somehow must use the literature as it is orranized to estimate Pfchemicals)dcharacteristics). The calc;lation comes from the right-hani side of the equation. P(characteristicsle(chemical). Some information about the numerator of the equation comes from knowing the ohvsical characteristics occurrine with chemicals. However. io estimate the actual probahilitiof a particular set of physical properties, given a specific substance, much more work is required. Certamly, handbooks and catalogs list the properties of chemicals. On the other hand, these lists are merely general and only relate the prohahility a characteristic ocVolume 65
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curs with the pure chemical. The chemist may know 1,3dichloropropane is an irritant. The generator, that is, the person u,hu supplies the unknown, even may know their material is an irritant, lxds around 100 OC, and is R chlorinated solvent. Even if all the characteristics were known rP = LO), a chemist could have an unhappy experience concluding the analysis a t this point. Mixtures and solutions have many ways to mask the properties of chemicals. There may be a dozen chlorinated solvents that are irritants and have boiline ranees from 90-110 OC. ~ ( c i e m i c a l )To . proceed with the analysis, the chemist needs to know the freauencv of the susnect chemical in the population. Chemists often are reluctani to deal with probabilities of this type. The clear liquid with ice in the lab beaker may he water, the most abundant and hence the most probable chemical. What chemist, thirsty though they may be, would drink the liquid? There is excellent data on the production of chemicals from the Commerce Department and other sources. Chemists may consider this type of data in evaluating an unknown, hut this information is low on the hierarchv of deductive reasonine. ~ ( c h a k t e r i s t i c s )T. o estimate the demoninator of the rieht-hand side of the eouation. one considers the ~robabilitGhat thepropertiesofihe unknown could becauied by any of the ootential chemicals. The ~robabilitsmust hecalculated for kach chemical, and all the prohahili&es must be added together. That is, for every possible chemical, one must calculate P(characteristics)g(chemical) X P(chemica1). In addition to involving all the problems discussed in the previous paragraphs, thetask is fuither complicated by the number of chemicals to be considered. There is a further probability that individual chemicals in the unknown have reacted to form hybrid molecules. The calculations obviously are simnlified hv reference to other data about the material. such as source iGformation (if such information is available), but in manv cases.. the . oossibilities are verv. larae. .. In summary, there is poor int'urmation, at best, about the individual Darts oithe orubabilitv formula. Even if the probabilities could be improved, a Eomputer tied into several data bases would have to he used for each analysis. The ability to use computers for such work is rapidly becoming more practical ( 4 ) , but it is not certain the results would he accurate. The mathematical approach thus leaves the chemist with three major obstacles: the amount of data to be considered, the need to interpret characteristics even though chemists are trained to understand chemicals, and finally, the need to manipulate probabilities. If a probability approach as simple as Bayes's theorem raises this many obstacles, i t is doubtful that more sophisticated models could be used to describe how chemists formulate an analytical logic. ~
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A Nonmathematical Approach The task of organizing widely diverse, extensive, and sometimesrontradirtory data toirriveat asucressfulanalysis is common to many professions.'l'he probabil~tyequation cited in this report was patterned after a compelling and incisive analysis of processes by which physicians arrive a t a medical diagnosis (5). I t seems likely the examination could be applied to a jurist's approach to a legal question, or a business a .~.n r o a c hto a financial analvsis. In each case, whate\,er the mental process, people come to the right decision in the maioritv of cases. Chemists have been eauallv surcessful. clinic2 tests save the lives of millions of people daily. Forensic chemistry is keeping pace with law enforcement needs, and hazardous wastes for the most part have heenstoredand treated safely. A Model for Analytical Strategies
There appear to be six steps used toarrive at an analytical strategy: collation of the initial findings, selection of one or more essential finding, review of the c.ssential findings, edit202
Journal of Chemical Education
ing the list, choice of laboratory tests, and validation of the results. (1) Collation of the Initial Finding. A finding is any sinele niece of information about the analvte. The observation ;ha; a material is a viscous liquid co&ists of at least two elementary findings. In a typical case the chemist is presented with hundreds of findings, most of which are negative. The analvte does not smoke on exposure to air: i t ~robablvis not an ai;.reartive chemical. Thesnalyte roulb "or be haloaenated solvent "x" htcause the plastic drum containing the solvent would be dissolved by chlorinated solvent "x",-and so on. The chemist is evaluating also the source of the preliminary information about the unknown. Experience shows certain eenerators are reliable. know how tocollect a snecimen without contamination, and know how to preserve it. If they have to euess about a material. the euess is carefullv aualified. 0n"the other hand, people wiil slap labels od poorly characterized and o r e ~ a r e ds~ecimensin an effort to dispose of their material ~uickly.~ h clinical k laboratory frequ&tly finds elevated blood glucose levels in wecimens from clients who are "certain they followed dietapy instructions before they gave blood." Although the glucose level is medically unexplainable, the patient knows he or she "didn't eat breakfast and didn't put sugar in their coffee." The analyst even may decide not to analyze a specimen if there is any suspicion a sample, a drug test, for example, was not collected or labeled according to the rules for the chain of custody. The chemist in such cases has, a t the bare minimum, a orofessional obligation to flae the report. During the coiation the size of the task is being reduced into manageable problems. A wide variety of observations may be grouped into the category "corrosive", for example. Aseries of abstractions capture the bitsof information
