The Inexact Imprecise Science of Trace Analysis L. B. Rogers University of Georgla, Athens, GA 30602 Most laymen and many scientists view chemistry as a discipline in which one can routinely make highly accurate and very precise measurements. The data are expected to be without bias and very reproducible if performed hy trained scientists using good techniques. However, in the area of quantitative trace analysis, the uncertainties become relatively large and, in some cases, are nearly the same size as the concentration or amount of the suhstance that is being measured, a situation quite comparable to the one for which the Heisenberg uncertainty principle applies. In any given procedure, there are many factors that lead t o low results throueh loss of the soueht-for snecies and. likewise. other factors that lead to high;esults irom unexpected soukes of contamination. The overall effect in anv eiven series of reolicates is that the actual combinations oi?osses and contahinations mav vaw widelv and, hence, the results mav show a very large coefficient of variation. Statistics tells us that the coefficient of variation can be decreased by making larger numbers of measurements. Unfortunately, i t is often impossible to obtain more than two or three samples or. in other cases. the cost of makine a sinele analysis may he so high that, even if plenty of sample is available. the auestion of runnine" a laree number of r e ~ l i cates is out of the question. In addition. one alwavs has t o make the implicit assumption that the Aeasuremknt deals only with the species he&g soueht. One tries tominimize the oossibilitv that an interference is partially or entirely responsible for the measured sienal hv resorting to the followine . steps. . First, one tries to anticipafe from the nature of the sample itself what rompounds might be present that could interfere. Apprupriate Bteps are then takkn to minimize or eliminate thatinierference. Second, classical quantitative analysis tells us that a second. as nearlv independent method as ~ossihle.should he used td check the anhytical results. unrortunatkly, in the field of trace analvsis. esoeciallv when one is trvine to work near the level of the detection rimit, there ma;ozy he one method that has the reauired sensitivitv. Hence. one usnallv assumes that the signalbeing measured is derived only from the soueht-for species. However. as the concentration (or amountr of the s & ~ ~ h t - f species or goes lower the possibility of encountering interfering species increases. A knowledeeable analyst is,-therefore, forced to he cautious to an extent that those not intimately acquainted with the additional difficulties of trace analysis find difficult to understand. Even many scientists who are familiar with the vagaries of trace analysis as seen in their own laboratories are unacquainted with the difficulties encountered in interlahoratory measurements of presumably identical portions of a given sample. New difficulties arise from different histories of the s a m ~ l e s(as a result of beine shipped .. or carried to different laboratories), differences between the ways in which the scientists perform the stated procedure, and differences between the opportunities for contamination and loss in those laboratories. Furthermore, there is another factor that many chemists who have not engaged in interlahoratories studies fail to appreciate. When a person knows a sample is a "marked" one; even though thd answer is unknown, the result of that analysis is almost invariably better than when the penon does not recognize the sample as one that requires special effort. Hence, an evaluation of the ev-
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Table 1. Maximum Number 01 lmpurllles, Each at a Given Level Glven: 99.999% pure material.
1 species 10 species lo4 species loe s~ecies
eryday performance of analysts requires that truly blind samples, similar in intent to the "double blind" samples used in clinical studies, he run. Characterlstlcs ot Measurements General Concepts I have chosen not to deal with statistics hut only to remind the reader about the meanings of the terms of accuracy (closeness of aereement between the experimental and the '.trueMresults);precision (extent of agreement between the different experimental results) and interference (miaidentification of the signal from another suhstance that from the sought-for suhstance). I t is important to note that one never knowingly includes the nignai irom an interference as part of theoverall signal. One houes that hv runnine calibration curves in a matrix that simulates the sample(srin question, one has eliminated the need for concern about any interference. However, clinical chemists are well aware of the fact that major changes in the compositions of hlood fluids are found when a patient is under stress, hungry, has just eaten, or has taken medication. Similarly, environmental chemists know that the composition of a river or a drainage ditch can change dramatically when i t rains or as one goes from the edge to the center or from the surface toward the bottom of the stream. As a result, new and unexpected substances mav he introduced into the respective streams that may chanie the probability of finding'an interference when usinga "rriedand true"method ofanalssis. Hence, the timing and the site as well as the method of the sam&ng may have critical impacts on the analytical result that is obtained. Likewise, the true meanings of the results are less
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,.loll?
The concentration level of the sought-for suhstance also becomesan extremely important factor that affects the likelihood of encounterine false sirnals from interferences. Most specialists in material science are happy to end up with a substance that is "five nines" pure, like that shown in Table 1. Such a material has a total of 10 parts per million of impurity. Note that, as the concentration of each impurity decreases, the number of possible interferences increases. If one goes one or two orders of magnitude lower than shown in the figure, it is possible to include every suhstance that has ever been made in a lahoratorv. Hence, as one approaches zero concentration, one is dealing with an increas&ly difficult situation in attempting . . to rule out possible interferences that can lead to the wrong a)ncluaiona. The history of analysis seems to show that the rate ar which the nensitivity improves often outpaces the rate a t which the proven selectivity improves.
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Volume 63 Number 1 January 1986
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The Measurement Process Individual Measurements. Signal-to-noise is a term that is frequently used to describe the size of the signal relative t o the uncertainty (standard deviation) of the base line in a blank. The recommendation has been made ( I ) that any signal that is less than 10times the standard deviation of the noise should not have quantitative significance attached to it. Instead, it should only be reported as "detected". Under snch conditions, one should not be surprised to find that replicate portions of a given sample produce widely different signal-to-noise ratios. In fact, one should not be surprised to find that a signal may be detected in one portion and not detected in another portion or that the signal from a "blank" is larger than that from a sample! This reflects the fact that the "limit of detection'' is not a well-defined concentration or amount hut instead represents a relatively wide region of uncertaintv (2).The contrast between the real world and the ideal w ( d d is'illustrated in Figures 1 and 2. h'evertheless, scientists freauentlv make the mistake of cxtrauolatine from relatively high c o n c h a t i o n s t o the "limit of dktection" and treatineit as thoueh it were known to two or three sienificant figures. Standards. Wherever possible, a Standard Reference Material (SRM), available from the National Bureau of Standards, is used as the primary standard against which all procedures and instruments are c a l i b r a t e d . primary standard is usually very close to 100% in . purity. . However, it is often possible for day-to-day requirements t o use certified secondary standards, many of which are issued by the National Bureau of Standards or other standards organizations. For example, a standard steel, of a composition close to one that is to he analvzed in the unknowns. can serve to assure the chemist that'the measurement syste? has been calibrated and the roba able interferences dealt with adequately. Calibrations. Ordinarily, a procedure or an instrument is calibrated by preparing samples containing different amounts of a primary standard so that one can then make a curve for either the amount recovered or the signal size versus concentration. The signals are measured in an ahsolute fashion relative to appropriate blanks. In some cases, however, there may be matrix effects which one attempts to minimize hv emulovine either the internal standard method or the metiod i f sianiard addition. The internal standard method uses calibration solutions nrenared in much the same way as in the first case excepi &at a second related substance of fixed concentration is Dresent. Instead of m lotting the signal for different coneentiations of the songht-for suhstance, one plots a ratio, the signal for the sought-for substance divided by the signal of the added reference. Such
an approach has been used for many years in measuring the sodium and ~otassiumcontents of blood nlasma. There the viscosity of the sample results in a greatly different intensity for the sodium line as measured bv atomic emission compared to the intensity for the same concentration of sodium in distilled water. By diluting a given volume of blood plasma with a standard volume of a known concentration of lithium, an element not normally found in blood plasma, one hopes that the signal for each of the elements will he affected to the same relative extent by the change in viscosity. The technique of standard addition is also employed for the same reason. After measuring a sample for the desired suhstance, a known amount uf that same substance is then added to the sample and the new signal level determined. One assumes that the difference in signal is linearly related lo thechange in concentration of the substance as a result uf the "s~ike"that has been added. Hrnce. one can calculate the concentration that produced the oritinal signal. Generallv, the results obtained bv either the internal standard or the standard addition method are likely t o be more accurate than data based upon a calibration curve DreDared nsine a i t is important to note that neitheLof pure solvent. these methods can correct for any part of the sienal that comes from an interference in the b r i g i d sample.~ence,if an interference is contributing any or all of the signal from the original sample, the use of either the standard addition or internal standard method can do nothing to inform the chemist of that error. That is whv it is hiehlv desirable to have available for use a second Lethod that is as nearly independent of the first as possible. In that case, it will, it is hoped, respond differently to the interferences. Clinical chemists and immunochemists. who are often handicapped by the absence of primary standards, are well acquainted with snch discrepancies. In addition, they are familiar with the fact that when two methods and/or two types of apparatus are compared over a wide range of concentrations, most of the signals from a given type of sample analyzed by each of the two methods mas be proportional overthe entire range but not necessarily those f o r d of the samples (see Fig. 3). This implies that for some samples an unknown interference is contributing to or subtracting from the signal obtained by one procedure but not the other, i.e., one or moreunknown interferine s ~ e c i e as m e a r in the fluids of some patients but not others.%ose dat'a'suggest that one ought to have available a third method for referee use in such samples!
ow ever,
LAWYERS WORLD Inereoring Concenlmtion w Amount D o n not szceed limit
Exceeds h i t
t
Reguiatwy Limit'
increasing Comatmtion or h o m t
PHYSICAL SCIENTISTS' IDEAL WORLD increasing Concentration or Amount Lower limitb
3 Upper limitb
Figure 1. The real world of measurement. a"S~metimesfound represents Emich's "reglon of uncertain reaction:" location of a oartlcuiar result lor the averaae of a arouo) .. within the reoion depend$ on the panicuiar combinations of ndeterm "ate errors wothln each ponion of lhe overall sample that is measured. 'The exact location 01 the lower I mil depends on lhe agreed-upon statistocai level of significance and the number of replicates measured. Reproducibilities in quantitative measurements will reflect the closeness of the sample content to the upper llml and, also, the width of the region of uncemln reaction.
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Journal of Chemical Education
I
Mvrr detected
1 t
A I w 11 dateckd
Detection Limit" Figure 2. The lawyer's world contrasted to lhe ideal world of the physical scientist. The lawyer's world features an absence of the laws of probability;ail uncenainty is anributed to human errws. 'Both the "regulatory llmiv' and "deteclion l i m p are an inflniieslmallythin line. dThe "detection limit" is defined by one event in "one-hn" biological theory assuming no repair mechanism.
Interlaboratory Measurements Most chemists who have not participated in interlaboratorv collaborative studies of the tvoe lone suoervised bv the ~ ~it~ , Association of Official ~ n a l ~ t i c' aCi h e m ~ s t s ; ~f&d incredible that comoetent chemists of long- exoerience . should disagree by an order of magnitude (or more) when analvzine s u ~ ~ o s e didentical lv ~ o r t i o n sof a eiven samde. (In ~achiab&atorythe chemists calibrate their proced"res and instruments against primary standards before measuring the substance in replicate portionsof asample.) A typical set of data (3) is illustrated in Figure 4 which shows the results of a study made in the early 1960's by the Taft Sanitary Engineering Center in Cincinnati, a predecessor to the U S . Environmental Protection Agency. This figure reports the average values found by different laboratories when three portions of a sample of unknown concentration
were analyzed after the chemists in the laboratory each had calibrated their procedure against a primary standard. The fact that several methods were used for the determination sueeests that the bias between the amount ~ u into t the sample and the average amount found was not an analytical error but a discreoancv arising from the handlina of the sample before it was analyzed b; those laboratories.~inally, to share in the excitement of being a regulator or one whose production process is being regulated, one needs only to select a t random the data from two of the laboratories and then assume that the regulatory limit is either the mean for all of the laboratories or is a value randomly selected from those ior the remaining Ialwratiries. A better grasp of a typical relationship between the corfficimts of variation fur "within" and "lwtneen" laboratories can be obtained from a specific example. In Table 2 are summarized the data reported by several laboratories in Italy for measurements of low levels of dioxin. Note how the coefficient of variation increased upon involving a second person in the same laboratory-and then increased further upon going to more than one laboratory. T o go one step further, it is interesting to speculate on what those coefficients of variation might have been had the
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Table 2. Dloxln Measurementsa
Figure 3. Comparison of two independem melhods. Method 1 Is low at large Method 2 includes an unknown imerference. Usas of standard addition ("spiking") andlor internal standard techniques fall to correct for direct inteiierencss. V ~ U B Sor
AVERAGE
AMOUNT
Operating Procedure
Coefficient of Variationa
Recovery of standard "spikes" 1 person 2 or morer 2 or m e d
8517%b i 5% i 10% i 26%'
< > >
*diDomenicoel al.. Anal C h . 51,735 (1979) 6 Stated to be the 99% confidence level aner -5% anllers have been dlscardsd. within one ~aboratory. d T 18bmtorie~ ~ ~ or cloaea two out of mree. '95% confidenm level for 0.1-1.0 pa: value is larger for mller amounts.
RECOVERED.O.14
MGlL
DIPHENYLCARBAZIDE W l T H PERMANGANATE-AZIDE OXIDATION DiPHENYLCARBAZlDE WlTH ALK-HYPOBROMITE OXIDATION N D I P H E N Y L C A R B A Z I D E WlTH PERSULFATE OXIDATION DIPHENYLCARBAZIDE WlTH UNSPECIFIED OXIDATION DIPHENYLCARBAZIDE WlTH N O OXIDATION B DIPHENYLCARBAZIDE U N S P E C I F I E D I3 S P E C T R O G R A P H 0 NOT SPECIFIED
c,-
LABORATORY
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NUMBER
Figure 4. Results of a study by IheTan Sanitary Engineerlngcenter of the average values found by different labaraforles for samplesof the same unknown. Details are given In text.
Volume 63 Number 1 January 1986
5
chemists not known that they were analyzing "marked" samples that were also being analyzed by other lahoratories. John Liddle, a pathologist a t the Center for Disease Control, found ( 4 ) that, after an extended period of practice, a group of lahoratories were able to analyze a standardset of samples with an acceptahle standard deviation for their pooled measurements. However, when he took those same samples and ran them through again as routine unknowns, the number of lahoratories that obtained "acceptable" results fell by 50%. His results clearly demonstrate that even though the chemists did not know the "correct" answers for the original test samples, they took extra care in performing those analyses so that those data were not representative of their everyday efforts. In a clinical laboratory that handles hundreds of samvles a dav. no one can he expected to devote extraordinary attention to each and ever; sample. Nevertheless, i t is the everyday ca~abilitvthat one is trvine to assess rather than a level bf eiceptional The Real World I t is clear that an analysis of an unknown sample from the r t d world can be quite different from that of its>ounterpart prepared in the laboratory. First, it iicrucial that thesample he taken in such a way as to answer a carefully phrased, specific question. Such a simple statement is often very difficult to realize in practice in spite of the ease with which it can be stated. Second, i t is important to recognize that the electronics industry, where contaminants must he controlled a t levels of the order of parts per billion (and, in some cases much lower), has had to resort to very expensive cumbersome, clean-room techniques. As the regulatory limits for maximum allowable amounts of chemicals go to parts per billion and lower levels, the same techniques and precautions must he taken in the analytical lahoratories in order to improve the reliabilities of the ;esults. I t is important for the public as well as regulatory officials torecomize the extraorcosts-;f such a task. dinary scientific demands-and Third, the coefficient of variation to he expected is auite difierent for samples prepared within agiven-lahorator;and thmr that come from the real world outside that laboratory. Therefore. it seems wise to establish the extent of azreemeit to be expected between the results for two lahoralories on the "same" s a m ~ l eas a crucial sten to he taken on the equivalent of "double blind" samples before an "acceptable" or "reasonable" level is vromuleated as a remlatorv limit. Unfortul ately, inappropkate data andlor ha: data are generally considered to be acceptahle in periods of great stress and emotion. Fourth, the fact that real-world (truly un-
6
Journal of Chemical Education
known) samples have correspondingly greater chances for giving misleading results as a result of signals from interferences as the levels of concentration are lowered must he recognized. Hence, the possibility of taking "corrective" actions, either for development of a product or for regulatory purposes, based on misleading, incorrect data becomes correspondingly more probable. As a result, unnecessary costs may he incurred. This problem reflects the unfortunate feature about a real-world sample-that the "true" result is never known. The quality assurance steps that have long been practiced by the AOAC (5)for increasinr the reliabilitv of interlaboratory analytical data are needea the most when decisions are to be based upon analyses involving trace concentrations or amounts of substances. I t is clear from regulatory history of the past 30 years that managers of industrial processes, regulators in eovernmental aeencies. and lawvers dealine " with regulations have much to learn about handling the uncertainties that are insenarablv hound to chemical analvses for trace levels of chemicals (6,-7).General guidelines h&e been recommended bv a erouv within the American Chemical Society ( 6 )that haveieen published in a report. R e ~ L I l a t 0limits ~ for some chemicals mav alreadv have reachkd lev& where nontraditional actionsheactio& may be required on the part of regulators in responding to demands by the public that existing limits be moved to still lower levels. As indicated earlier, the closer one gets to the unattainable goal of zero concentration, the greater is the uncertainty of any scientifically based conclusion about the concentration actually In any case, the credihilities of any new limits will he much higher if they are established hv an exvert. disinterested third nartv. such as the AOAC. ajter appropiiate supporting datahave been obtained rathe; than before (6).
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Literature Cited (1) ACS Committee on Environmental Improvement, "Principles of Environmental Anal. ~8is: A w l . Chem., 55.2210-18 (1983). (2) Emieh, F., Ben, 43.10 (1910);through Feigl. F. "Chemistryof Specific, Selective and SensitiveReadions:Oesper.R. E., Trans., AeademicPree+NcwYork, 1949,p. 14. (31 "AnalyticslReferrneeSemiceTraininpPropram,ReportofWater Metals."No.2, U S Dapt, of Health. Education and Wdfare, Robert A. Tdt Sanitary Engmserh Center. Cincinnati. OH L9EZ. (4) Liddle, J. A , thmugh Msugh, T.H., 11, Science, 216,490 (1982). (5) Garfield, F. M., "Quality kssurmce Principles for Anslytical Lsborstorica." Assodation of Official Analytical Chemists, Arlinpton, VA, 1984. ( 6 ) Ad Hoe Subcommittee Dealing with the Scientific Aspects of Regulatory M a - . rnent*, ACS Joint BoardICouncii Committee on Seience,'4m~~ovina the Reliability and Arreptability of Analytical Chemical Data wed for P U ~ I ~ C P U & ~ : May 16, 1982:see also Cham. En& News. 60(23), 44 (19821. 17) R0zers.L.B.."Seminar of Prioritv Pollutant*. Januarv 1S.1980!'ChemiealMmufae-
