REPORT
The Hierarchy and Relationships
Properties
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Mlguel Valcdrcel and Angel Rlos Department of Analytical Chemistry University of C6rdoba 14004 C6rdoba, Spain
The quality of the analytical information produced in a laboratory depends on the quality of the information available t o managers as they defme the analytical problem, design the analytical process, and adjust ita features so that the results produced meet the required objectives (e.g., compliance with laws, norms, or quality control of products and systems). It is important to have a clear understanding of analytical properties such as accuracy and representativeness as well as their relationship to quality in t h e analytical process and to the results. These two facets of analysis are frequently dealt with inconsistently, resulting in confusion in laboratory work and in communications with clients or service users. The purpose of this REPORT is to 0003-2700/93/0365-781ArSC4.00/0 0 1993 American Chemical Society
establish a hierarchy for analytical properties, illustrate their mutual relationships, and describe how the social and economic considerations of a given analytical problem affect the dominance of some properties over others. As we will see below, dealing with analytical properties in isolation when designing strategies to address specifk problems is often inadequate a n d produces erroneous results. Types of analytical properties Quality in the analytical results, the primary goal of analytical chemistry, relies heavily on two capital analytical properties: accuracy and representativeness. Accuracy means consistency between the results obtained and the actual concentration of the analyte in a particular sample; representativeness refers to consistency between the results and the analyzed sample as well as between the results and the definition of the analytical problem. Capital properties rely on another
group of analytical properties that we will call basic properties. They determine the quality of the analytical process both inside the laboratory and outside the laboratory during sampling. Basic properties are sensitivity, selectivity, precision, and sampling; their definitions can be found in a numher of analytical textbooks and monographs. The analytical process is also limited by seemingly less signiiicant accessory properties. These properties, however, often have major practical implications. They include expeditiousness, cost-effectiveness, and personnel-related considerations, all of which affect laboratory output. Figure 1shows the two essential components of analytical quality and displays capital, basic, and accessory analytical properties in a hierarchical manner. It also outlines the generic objectives of present-day analytical chemistry: obtaining larger amounts of analytical information of a higher quality by expending less material, time, and human re-
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REPORT sources;minimizing risks, and incurring the smallest expenses possible (1).Whereas capital analytical properties are associated with results, basic and accessory properties are related to the analytical methodology used. Analytical properties, whether viewed individually or collectively, are not independent of one another. In fact, they exhibit mutual-and occasionally opposing-relationships. Attempts to optimize a given analyt-
ical procedure should, in principle, be aimed a t the capital properties. The maximum possible sensitivity, selectivity, and precision should be achieved, a n d proper sampling should be carried out. However, emphasis is often placed on saving or minimizing time, costs, materials, reagents, labor, and hazards, which leads t o greater expeditiousness, cost-effectiveness, automation, and personnel safety and comfort. The balance between the objectives as de-
Proceder
Figure 1. Goals of analytical chemistry and their relationships to analytical quality and analytical properties.
FlgUm 2. Analytical tetraneara. 782 A * ANALYTICAL CHEMISTRY, VOL. 65, NO. 18, SEPTEMBER 15,1993
picted in Figure 1 determines to a great extent how analytical procedures are designed. Analytical tetrahedra The most straighfforward and intuitive form of graphically displaying analytical properties involves two tetrahedra that share a vertex and can be of varying sizes relative to each other (Figure 2). This illustration provides a useful means of distinguishing among the three principal groups of analytical properties, establishing a hierarchy, and determining symbiotic and opposing relationships among them. Figure 2 also includes sampling, which determines representativeness. The vertices of the main tetrahedron (left) depict sensitivity, selectivity, and precision; one of its faces represents accuracy, which relies on these three basic properties. This tetrahedron, together with representativeness of sampling, h a s t h e greatest statistical weight on analytical results and is connected with the objectives of obtaining more and better information. The secondary tetrahedron (right) has vertices depicting the accessory analytical properties; one of its faces represents laboratory productivity. This tetrahedron is related to the objectives of minimizing time, costs, labor, and hazards. The balance among analytical properties illustrated in Figure 2 will be shifted by the specific elements of the analytical problem addressed (e.g., result quality is always in conflict with productivity). The balance between two competing sides represents a compromise and defines the competitiveness of the analytical laboratory concerned. For example, although a laboratory may be more competitive if it can obtain results in a short time, some accuracy may be sacrificed. Each laboratory should determine the most competitive position of the equilibrium to address a particular problem. Shifts in the balance depicted in Figure 2 can be classified by three groups according to whether one, two, or three analytical properties are to be prioritized. The initially regular tetrahedra become irregular prisms when a vertex, edge, or side is pulled, lengthened, or expanded while others are pushed, shortened, or contracted. Accuracy and representativeness As indicated previously, overall quality in analytical chemistry is determined by accuracy and representa-
Flgure 3. Mechanisms for increasing accuracy by enhancing basic analytical properties. (a) including weparation techniques to preconcenlrale anaiytes of imrest and remove intefierences enhancss one or more of the three basic analytical properlies. (b) increasinganalysis predsion muits in increased accuracy.
tiveness and depends on the quality of the work performed outside (sampling) and inside the laboratory (the analytical process). The influence of sampling on analytical quality cannot be overstated. Proper sampling is essential for achieving the degree of representativeness appropriate to the analytical problem and thus for providing quality results. Accuracy in the analysis of a nonrepresentative sample is meaningless. For example, an accurate determination of the fat content of milk in only a few randomly selected packages by use of validated methodologies based on modern instrumentation is not useful analytical information if the objective is to determine the fat content of a batch of 10,000 packs. Appropriate statistical sampling must be carried out if the information produced is to be representative of the problem a s a whole. Another example involves t h e b l d potassium concentration deter-
mined from a sample taken from a patient more than 1 h after a heart attack. The sample cannot be considered representative of the patient's blood potassium concentration a t the time of the heart attack. Representativeness is therefore an unavoidable prerequisite and the bottleneck that controls the entire analytical process: No other analytical property can be justified in the absence of representativeness. Accuracy is the analytical property most closely related to laboratory work in which the chemical composition of a known sample is determined. It is complementary to representativeness because i t allows specific analytical determinations to be made about a sample. It also validates representativeness because, however representative a sample may be, it is useless if the analytical information about it is inaccurate. Although i t is rather difficult to assess representativeness, certain statistical approximations can be applied to sampling techniques that make them easier to implement and more reliable. In many cases, it is imperative to talk with individuals both inside and outside the area of interest and to investigate a variety of techniques to ensure a properly defined analytical question that will provide results representative of the scientific, economic, or social problem addressed. Accuracy, on the other hand, can be evaluated much more easily by, for example, use of certified reference materials. Accuracy and basic analytical properties Accurate results rely on adequate sensitivity, the absence of interferences, and reasonable repeatability/ reproducibility (i.e., low uncertainty) for the analytical method used. Thus in Figure 2 the vertices of the face of the main tetrahedron, which represents accuracy, coincide with the three basic analytical properties. In fact, if the analyte concentrations in the sample are lower than the detection or quantification limits achieved, the analytical results will not be consistent with these limits. Any perturbations arising from positive or negative deviations in the analytical signal, whether of an additive or multiplicative nature, will also shift the results from the actual values. The tetrahedron edge bound by the sensitivity and selectivity vertices can be markedly lengthened by including separation techniques in the analytical process; through preconcentration and interference re-
moval, such techniques indirectly enhance one or more of the three basic analytical properties (Figure 3a). Liquid-liquid extraction is a separation technique widely used for this purpose. Although a given analytical p m dure may be highly accurate but not precise &e., the mean of a set of disperse results obtained for the same sample may coincide with the actual value), accuracy usually depends on the absence of systematic errors arising from low levels of the basic analytical properties and from the so-called human factor and indeterminate (random) errors. Highly uncertain results are also generally not accurate. Thus increased precision results in increased accuracy (Figure 3b); the former can be achieved by simplifying or automating the analytical process (2).For example, the use of an automatic sample/standard introduction system in electrothermal vaporization atomic absorption spectroscopy ensures greater preci sion in routine analyses compared with the level of precision achieved with manual introduction.
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Relatlonshlps among bask analytlcal propertles Figure 4 depicts the opposing relationships among the three basic analytical properties. Enhancing one usually can be achieved only a t the expense of the other two. The central equilateral triangle represents a balanced situation and can be distorted to an isosceles or scalene triangle, depending on which property is favored. For comparison, triangle areas have been kept constant. The most salient relationships among the three properties are discussed below. Precision and sensitivity. It is well known that precision decreases as analyte concentrations decrease.
Figure 4. Relationships among ba! analytical properties.
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REPORT Figure 5 shows an example of the results from intercomparison food analysis experiments in which the coefficient of variation increases exponentially with decreasing analyte concentration (3). Consequently, a highly sensitive method will also be highly variable when applied to trace and ultratrace determinations. Errors off 10% in the determination of a few nanograms per milliliter of a drug in blood are quite acceptable; however, errors made in determining the same drug a t the milligram-per.gram level in a pharmaceutical preparation should not exceed f 2%. Incorporating an analytical separation technique to indirectly enhance sensitivity and to facilitate the determination of analyte concentrations below the detection or quantification limit of the analytical method used complicates preliminary operations and increases the time spent by the researcher. In addition, precision is diminished. Determination of trace cadmium in seawater by direct application of a selective spectroscopic technique such as graphite furnace atomic absorption spectroscopy or inductively coupled plasma atomic emission spectroscopy resulte i n errors smaller t h a n those obtained when a preconcentration procedure such as liquid-liquid extrac-
Figure 5. Relationship between the precision and the concentration level of the analytes to be determined in the form of a Horwitz graph. (Adapted with permission from Referem 3.)
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tion or ion exchange is used before spectroscopic analysis. The standard deviation of the estimate for a calibration curve establishes a statistical relationship between precision and sensitivity: The higher t h e sensitivity (i.e., t h e greater the curve slope, as defined by IUPAC), the higher the precision achieved in the analyte determination. In fact, a t a given signal level the more sensitive method (Figure 6a) provides a less uncertain result than does the less sensitive method (Figure 6b), provided both calibration curves have similar standard deviations of the estimate. Also, for a given curve, the highest precision lies in the central portion and decreases toward the ends (quantification and upper limit, respectively). Detection and quantitation limits, two ways of defining sensitivity, are calculated via a precision-related parameter: the standard deviation of the blank. The relationships between sensitivity and precision discussed above contribute to the uncertainty of the measuring analytical technique used. Thus weighings on an analytical balance are subject to fixed errors (e.g., f 0.1 mg) that will affect t h e precision of t h e measuring method to an extent inversely proportional to the weighed amount of sample, reagent, and reaction product. With other analytical techniques, the highest possible precision i s achieved over a given analytical signal range; such is the case with W-vis photometry, where the zone of minimum error is bound by absorbance values between 0.2 and 0.8 AU. Sensitivity and selectivity. Notwithstanding their seemingly distinct natures, sensitivity and selectivity are also related and not always in an opposite manner. In fact, the difference between additive and multiplicative interferences lies i n whether the perturbation concerned affects the slope (sensitivity) of the calibration curve. The more sensitive t h e method used to determine a given analyte, the more a sample can be diluted to decrease the concentrations of interferences and hence minimize or eliminate their perturbations. This approach is widely known and exploited in the analysis of clinical/biological samples; sensitive methods call for high initial dilutions (1:10-1:10,000) to minimize the typical perturbations of macromolecules. Sensitivity and selectivity can be enhanced by similar mechanisms (4): chemical reactivity (e.g., by using or-
ANALMICAL CHEMISTRY,VOL. 65, NO. 18. SEPTEMBER 15,1993
Flgure 6. Relationship between sensitivity and precision in terms of the uncertainty involved at a given signal level in two calibration C U N ~ S of different slope. (a) More sensitive method. (b) Less sensitive method.
ganic r a t h e r t h a n inorganic r e agents); material separation (e.g., by combining preconcentration and interference removal, a s i n liquidliquid extraction and anodic stripping voltammetry); selection or alteration of the instrumental technique used (e.&, atomic rather than molecular optical techniques or the use of chemically modified eledrodes for potentiometric measurements); binary or ternary combinations of the above choices (e.g., pre- and postcolumn derivatization in chromatography, where chemical reactions are used to enable the separation and detection of the solutes, respectively); and uee of chemometric techniques in combination with one or more of the previous alternatives (e.g., multivariate calibration procedures). Newly emerging analytical laboratory instruments tend to incorporate these mechanisms to enhance basic analytical properties. The use of nonchromatographic continuous separation techniques and multichannel detectors as well as the development of hyphenated techniques-one part of which can be a type of chromatography-and on-line combined techniques are additional good examples in this context.
Selectivity and precision. The uncertainty inherent in the mechanisms described above for enhancing selectivity is related to the complexity of the analytical process. When several such mechanisms come into play, the indeterminate error arising from each is seen in the fmal result, and precision is diminished. Thus if the selectivity of the methodology in question arises from the detector used (e.g., in single- and multichannel atomic spectroscopy),the analytical process is simpler and higher precision is achieved. However, the precision is decreased when one incorporates new chemical reactions or a separation procedure to increase the selectivity because it expands the traceability chain. Using a separation technique to remove interferences introduces further uncertainty in the final result because the analytical process is being expanded or eomplicated. By automating the preliminary operations of the analytical process (2)or by using hyphenated techniques, human errors can be minimized. In fact, online combinations of separation techniques a r e effective means of i n creasing t h e overall precision achieved by using t h e combined techniques in isolation. Thus the coefficient of variation associated with the use of a supercritical fluid extractor and a gas chromatograph combined on line is lower than the summation of those obtained when the extraction and separationldetermination steps are carried out separately. Appropriate chemometric or simple mathematical treatments increase selectivity. Univariate calibration and differential kinetic methods (e.&, logarithmic extrapolation) (5,6)are two god choices. As a rule, the use of these methods results in poor precision-even poorer than that obtained from analytical separation techniques. However, one can use these methods to avoid some stages of the analytical process. Accuracy and accessory analytical propertles Designing an analytical method by which t o achieve high accuracy means that high levels of the basic analytical properties must be obtained a t the expense of the accessory properties. As can be seen in Figure 7a, the main tetrahedron is distorted when the area of the triangular accuracy face is increased, whereas the secondary tetrahedron is considerably shrunk by shifting those forces pointing toward the
Personnel
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(b) accessory analytical properties.
0 Figure 0. Relationships among the complementary analytical properties and the prevalence of one or two of them. Resulls of enhancing (a) cost-effectiveness,(b) cost-effenivenessand expdiliousneas, (c) expeditiousness.(d) cost-effectiveness and personnel safely/mrnforl, (e) personnel s.+ely/cornlon, and (I)expeditiousness and personnelsafeiylcomfort.
main tetrahedron. This situation reflects the priorities among the capital, basic, and accessory analytical properties in Figure 1. The opposite situation (Figure 7b) occurs when temporal, economic, and/or personal
aspects related to laboratory productivity prevail upon the quality of the results. Obtaining immediate analytical results in response to an urgent demand (e.g., in the clinical field) or
ANALYTICAL CHEMISTRY, VOL. 65, NO. 18, SEPTEMBER 15,1993
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REPORT c o n t r o l l i n g a process in n e a r r e a l t i m e entails sacrificing some accuracy. Thus some recent applications rely o n FT-IR spectroscopy to obtain accurate, reproducible results in as short a t i m e as possible with minimal sample handlingand manual involvement (e.g., on-line process cont r o l in m a n u f a c t u r i n g w o r k Occasionally, a timely ”yes or no” rep l y to indicate whether a given parameter i s above or below the tolerated l e v e l i s more i m p o r t a n t t h a n obtaining a n accurate analytical re; s u l t a few hours later. Sensors (8) and screening tests based o n immunoassay (9) are additional good examples. When economic constraints affect laboratories or when available equipment i s limited, the quality of the r e sults suffers. Acquiring and processing analytical signals manually w i t h poor-quality reagents and rudiment a r y equipment t h a t lacks adequate electronic w n t r o l adversely influence the accuracy of the results. Nevertheless, the best technical means are n o guarantee that results w i l l be accurate unless the analytical process i s developed properly, in compliance
The first step usually taken to cut laboratory expenses is to reduce, personnel. This results in a heavier workload lor remaining personnel and in a slower delivery of results (Figure Ea).
[a).
lncreasina IhrouahDut requires au menti; laboiaiory eciuipment a n i comdling staff to work harder (Figure Ec). Pe
brt
If political or trade union pressure takes personnel claims to extremes, costs immediately rise and throughput falls (Figure 8e).
ltiousness
If costs need to be reduced and throughput raised, the analytical process is frequently automated lully or partly. Automation results in staff dismissals and the assignment of greater responsibilities to the remaining analysts, who thus require retraining (Figure 8b). I personnel safety/wmfort is not critical to obtaining the analytical results, the staff will be under no pressure and none of the extraordinary and also costly means needed to mantain a high throughput will be required (Figure 61).
The laborato Lw et must be increased to maintain a%igh%rough t without alteflng personnel status (&re W.
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with established quality assurance norms (10). Accuracy is also affected by the human factor which, despite the high degree of automation currently available at many laboratories, remains crucial. The ease with which results are obtained from automatic analytical methods and the increasing isolation of instrument operators from the process foster operator errors because of overconfidence in automated equipment. These factors also diminish the attention given to, a critical evaluation of the results obtained. Other major human factors are operator comfort and safety precautions, the implementation of which occasionally entails sacrificing some accuracy to prevent hazards for the operators and those near them. Such is the case with routine analyses involving hazardous reagents or methods. Though the need for accuracy exists, methodology should be modified to avoid hazards and the possibility of accidents, and to minimize the need for the continuous attention of the operator. Accessory analytical properties The accessory properties at the vertices of the productivity triangular face of the secondary analytical tetrahedron also exhibit opposing relationships. The imposed or advisable prevalence of one or two of these properties distorts the equilateral triangular face and hence disturbs the balance among them. When an analytical procedure is designed to enhance one of the three properties-cost-effectiveness (Figure Sa), expeditiousness (Figure Sc), or personnel safetylcomfort (Figure Se)-the other two sides of the resulting productivity triangular face are markedly shortened. If two properties rather than one are favoredcost-effectiveness and expeditiousness (Figure Sh) or expeditiousness and personnel safetylcomfort (Figure 80 or cost-effectiveness and personnel safetylcomfort (Figure S d h t h e side of the remaining property is contracted. Examples of such situations appear in the box on p. 786 A. Quality compromises Meeting the demands imposed on the information produced by an analytical laboratory requires that a compromise be made between the two components of the analytical chemistrylquality binomial: external quality, which refers to the properties of the monitored product or service, and internal quality, which
deals with the analytical process and the results produced. External quality may result from compliance with legislation or quality requisites for a production process. It directly affects analytical quality, which depends on capital, basic, and accessory analytical properties. As we have seen, analytical quality can be approached in various ways, depending on the analytical problem. From a strictly theoretical point of view, the situation in Figure Sa can be considered ideal-at the least, one should reach the balanced situation shown in Figure 2. However, the facts may justify the situation depicted in Figure Sa for the analytical laboratory t o meet t h e demands posed by the analytical problem derived from the economic or social problem addressed. The current requirement that all laboratory activities be in written form necessitates managerial planning. In many cases this requirement is imposed by law, and often a company produces a quality manual whereby the specific priorities affecting the analytical properties graphically related by the two tetrahedra are to be established via standard operational procedures (SOPS). In R&D and in pharmaceutical industry laboratories, priorities are imposed by organizations such a s the Food and Drug Administration or the Organization for Economic Cooperation and Development in the form of Good Laboratory Practices. On the other hand, in analytical R&D laboratories, such as those a t universities where new analytical methods and technological innovations are developed, the goal is to characterize each of the analytical properties inherent in the new method or technique according to quality control norms. Final remarks In the foregoing discussion, we have strived to establish a hierarchy of analytical properties as well as their relationships to one another and the two analytical quality components. In addition, we have underscored the need t o accurately define objectives when designing analytical procedures. Although a number of the individual factors dealt with here are well known, they have rarely been considered together or in a systematic manner despite the fact that they are most likely the ultimate foundation of analytical chemistry. This view can be of use to basic and applied researchers in planning and managing laboratories as well as in teaching analytical science.
References (1) Valcarcel, M. Fresenius Z.Anal. Chem.
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(2) Valc6rce1, M.; Luque de Castro, M. D.
Auiomatic Meihods ofAnalysis; Elsevier: Amsterdam. 1989. DD. 13-23. (3) Horwitz,' W.; Kakps, L. R.; Boyer, K. W. J. Assoc. OK Anal. Chem. 1980, 63, 1344. (4) Valc6ree1, M.; Rim, A. Analusis 1990, 18, 469. ( 5 ) Martens, H.; Naes, T. Multiuariaie Calibraiion; John Wiley & Sons: New York, 1991. ( 6 ) Perez-Bendito, D.; Silva, M. Kineiic Meikods in Analytical Chemistry;Ellis Horwood: Chiehester, England, 1988. (7) Pandey, G. C.; Kulshreshtha, A. K. Process Control and Quality 1993,4, 109. (8) Murray, R. W.; Dessy, R. E.; H e w man, W. R.; Janata, J.; Seitz, W. R. Chemical Sensors and Microinsfrumenintion; ACS Symposium Series 403; American Chemical Society:Washington, DC, 1989, pp. 1-22. (9) Van Emon, J. M.; L6pez-Avila, V. Anal. Chem. 1992,64,79 A. (10) Taylor, J. K. QualityAssurance of Chemical Measurement; Lewis: Chelsea, MI, 1987.
Miguel Valcurcel (lefi) has been a professor at the University of Cordoba since 1976. He received his B.S. degree in chemistry and his Ph.D. in analytical chemistry (1971) from the University of Sevilla (Spain). Valcdrcel's research interests include the automation ojanalytical processes, flow injection methods, (bio)chemical sensors, nonchromatographic continuous separation techniques, and the implementation ofquality systems in the analytical laboratory. He is the author or coauthor of about 400 research papers, six textbooks, and three monographs. Angel Ri'os (right) is an assistant projesSOY in the Department o f A n a l y f i c a l Chemistry at the University of Cdrdoba. He received his B.S. degree in chemistry (1980) and his Ph.D. in analytical chemistry (1983) from that university. His research interests include automatedpow systems and the implementation and application ojquality principles in control and R&D analytical laboratories.
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