LOGOReporting Results and Reliability of Analyses

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2Reporting Results

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introduce

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The basic purpose of an analytical assay is to determine the mass (weight) of a component in a sample. The numerical result of the assay is expressed as a weight percentage or in other units that are equivalent to the mass/mass ratio. The mass (weight) of a component in a food sample is calculated from a determination of a parameter whose magnitude is a function of the mass of the specific component in the sample.

Some properties are basically mass dependent. Absorption of light or other forms of radiant energy is a function of the number of molecules, atoms, or ions in the absorbing species. Although certain properties, such as specific gravity and refractive index, are not mass dependent, they can be used indirectly for mass determination. Thus, one can determine the concentration of ethanol in aqueous solutions by a density determination. Refractive index is used routinely to determine soluble solids (mainly sugars) in syrups and jams. Some mass-dependent properties may be characteristic of several or even of a single component and may be used for selective and specific assays. Examples are light absorption, polarization, or radioactivity. Some properties have both a

Reporting Results and Reliability of Analyses

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magnitude and a specificity parameter (nuclear magnetic resonance and infrared spectroscopy). Such properties are of great analytical value because they provide selective determinations of a relatively large number of substances.

In this chapter, we describe conventional ways of expressing analytical results and discuss the significance of specificity, accuracy, precision, and sensitivity in assessing the reliability of analyses.

In recent years the metric SI system of units has gained worldwide acceptance. It has been recommended or required by International Union of Pure and Applied Chemistry (IUPAC), and the International Union of Pure and Applied Physics (IUPAP), as well as by an increasing number of scientific and professional organizations in the United States and by the industry and the trade. The SI system contains seven base units, two supplementary units, 15 derived units having special names, and 14 prefixes for multiple and submultiple units. All physical properties can be quantified by 38 names.

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In reporting analytical results, both the reference basis and the units used to express the results must be considered. For example, analyses can be performed and the results reported on the edible portion only or on the whole food as purchased. Results can be reported on an as-is basis, on an air-dry basis, on a dry matter basis, or on an arbitrarily selected moisture basis (e.g., 14% in cereals).

To convert contents (%) of component Y from oven-dried (OD) to an as-received (AR) basis, or vice versa, the following formulas are used:

Reporting Results)%100(

100%%

ODloss

YY

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To convert contents from an as-received basis to an arbitrary moisture basis, the following formula is used:

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To weight out a sample on an arbitrary moisture (AM) basis, use the following:

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To obtain % dry matter, subtract percentage of moisture from 100. If the moisture has been determined in two stages, air drying followed by oven drying, compute total moisture contents of sample as follows:

Where TM is the % total moisture, A the % moisture loss in air drying, and B the % moisture of air-dried sample as determined by oven drying.

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Tables, nomograms, and calculators are available to simplify calculations in expressing results on a given basis, or for weighing samples on a fixed moisture basis (e.g., 20% in dried fruit). In view of the very wide range in moisture contents in various foods, analytical results are often meaningless unless the basis of expressing the results is known.

Expressing analytical results on an as-is basis is wrought with many difficulties. It is practically impossible to eliminate considerable desiccation of fresh plant material. In some instances, even if great pains are taken to reduce such losses, the results may still vary widely. For example, the moisture contents of leafy foods may vary by as much as 10% depending on the time of harvest (from early morning to late afternoon). Similarly, the moisture contents of bread crust and crumb change from the moment bread is removed from the oven as a result of moisture migration and evaporation. Absorption of water in baked or roasted low-moisture foods (crackers, coffee) is quite substantial. In most cases, storing air-dried foods in hermetically closed containers is least

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troublesome. Once the moisture contents of such foods are determined, samples can be used for analyses over a reasonable period.

The concentrations of major components are generally expressed on a percentage by weight or percentage by volume basis. For liquids and beverages, g per 100mL is often reported. Minor components are calculated as mg (or mcg) per kg or L; vitamins in mcg or international units per 100g or 100mL.Amuunts of spray residues are often reported in ppm (parts per million).

In calculating the protein contents of a food, it is generally assumed the protein contains 16% nitrogen. To convert from organic nitrogen (generally determined by the Kjeldahl method; see Chapter 37) to protein, the factor of 6.25=100/16 is used. In specific foods known to contain different concentrations of nitrogen in the protein, other conversion factors are used (5.7 in cereals, 6.38 in milk). Heidelbaugh et al. (1975) compared three methods for calculating the protein content of 68 foods: (1) multiplication of Kjeldahl nitrogen by 6.25; (2) multiplication of Kjeldahl nitrogen by factors ranging

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from 5.30 to 6.38 depending on the type of food; and (3) calculation on the basis of amino acid composition, determined by chemical analyses. Up to 40% differences in protein content were found depending on the calculation method. There were, however, only small differences in mixed diets representing typical menus.

If a food contains a mixture of carbohydrates, the sugars and starch are often expressed as dextrose. In lipid analyses (free fatty acids or total lipid contents) calculations are based on the assumption that oleic acid is the predominant component. Organic acids are calculated as citric, malic, lactic, or acetic acid depending on the main acid in the fruit or vegetable.

Mineral components can be expressed on an as-is basis or as % of total ash. In either case the results can be calculated as elements or as the highest valency oxide of the element.

Amino acid composition can be expressed in several ways: g amino acid per 100 g of sample, or per 100 g of protein, or per 100 g of amino acids. For the determination of molar distribution of amino acids in protein, g-mol of amino acid residue per 100 g-mol of amino

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acid are computed. In trade and industry, empirical tests are often used. For example,

fat acidity of cereal grains is often expressed as mg KOH required to neutralize the fatty acids in 100 g of food. Acidity is often expressed for simplicity in milliliters of N/10 or N NaOH. The acidity of acid phosphates in baking powders is reported in industry as the number of parts of sodium bicarbonate that are required to neutralize 100 parts of the sample.

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The reliability of an analytical method depends on its (1) specificity, (2) accuracy, (3) precision, and (4) sensitivity (Anastassiadis and Common 1968).

Specificity is affected primarily by the presence of interfering substances that yield a measurement of the same kind as the substance being determined. In many cases, the effects of the interfering substances can be accounted for. In calculating or measuring the contribution of several interfering substances, it is important to establish whether their effects are additive.

Accuracy of an analytical method is defined as the degree to which a mean estimate approaches a true estimate of an analyzed substance, after the effects of other substances have been allowed for by actual determination or calculation. In determining the accuracy of a method, we are basically or calculation. In determining the accuracy of a method, we are basically interested in establishing the deviation of an analytical method from an ideal one. That deviation may be due to an inaccuracy inherent in the procedure; the effects of substances other than the analyzed one in the food

Reliability of Analyses

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sample; and alterations in the analyzed substance during the course of the analysis.

The accuracy of an analytical assay procedure can be determined in two ways. In the absolute method, a sample containing known amounts of the analyzed components is used. In the comparative method, results are compared with those obtained by other methods that have been established to gibe accurate and meaningful results.

The absolute method is often difficult or practically impossible to apply, especially for naturally occurring foods. In some cases, foods can be prepared by processing mixtures of pure compounds. If the mixtures are truly comparable in composition to natural foods, meaningful information is obtained.

Several indirect methods are available to determine the accuracy of analyses. Although these methods are useful in revealing the presence of errors they cannot prove the absence of errors. When a complete analysis of a sample is made and each component is determined directly, a certain degree of accuracy is indicated if the

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sum of the components is close to 100. On the other hand, an apparently good summation can result from compensation of unrelated errors in the determination of individual components. A more serious error can result from compensation of errors that are related in such a way that a negative error in one component will cancel a positive error in another component. This may be particularly important in incomplete fractionations. For example, the sum of proteins separated according to differences in solubility may be close to 100%, yet the separation of individual components may be incomplete or of limited accuracy.

In the recovery method, known amounts of a pure substance are added to a series of samples of the material to be analyzed and the assay procedure is applied to those samples. The recoveries of the added amounts are then calculated. A satisfactory recovery is most useful in demonstrating absence of negative errors.

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If the accuracy of an analytical method is affected by interference from substances that cannot be practically eliminated, a suitable correction can sometimes be applied. Such a correction is often quite complicated because the results may be affected by concentration of the interfering or assayed substance, or by their interaction in food processing or during the analyses.

Precision of a method is defined as the degree to which a determination of a substance yields an analytically true measurement of that substance. It is important to distinguish clearly between precision and accuracy. In industrial quality control, it often is unimportant whether analysis of numerous similar samples yields exactly accurate (i.e., true) information regarding the composition of the sample. The information may be useful provided the difference between the precise and accurate determination is consistent. The analysis that gives the actual composition (or in practice the most probable composition) is said to be the most accurate. For instance, direct and accurate determination of the bran content can be estimated directly from the amount of crude fiber in a flour. This

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estimation is based on the fairly constant ratio between crude fiber (determined by a precise, but not accurate, empirical method) and actual bran contents. Still simpler is the estimation of bran content from total mineral content or reflectance color assay of a flour.

To determine the precision of an analytical procedure and the confidence that can be placed on the results obtained by that procedure, statistical methods are used. The most basic concept in statistical evaluation is that any quantity calculated from a set of data is an estimate of an unknown parameter and that the estimate is sufficiently reliable. It is common to use English letters for estimates and Greek letters for true parameters.

If n determinations x1,x2,…….xn are made on a sample, the average is an estimate of the unknown true value . The precision of the assay is given by the standard deviation :

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If the number of replicate determinations is small (<10), an estimate of the standard deviation ( s ) is given by

The divisor n-1 used to estimate s is termed the degrees of freedom and indicates that there are only n-1 independent deviations from the mean. The standard deviation is the most useful parameter for measuring the variability of an analytical procedure.

If s is independent of x for a given concentration range, s can be computed from results of replicate analyses on several samples of similar materials. In that case, the sums of the squares of the deviations of the replicates of each material are added, and the resultant total is divided by the number of degrees of freedom (the sum of the total number of determinations, n, minus the number of series of replicate determinations).

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A complicating factor in determining the precision arises when the standard deviation varies with the concentration of the element present. Sometimes the range of concentration can be divided into intervals and the standard deviation given for each interval. If the standard deviation is approximately proportional to the amount present, precision can be expressed as a percentage by using the coefficient of variation (CV).

If the data show a varying standard deviation, transformation of the data into other units in which the standard deviation is constant is often useful. Two widely used transformations are square roots and logarithms.

Chemical analyses are made for various purposes and the precision required may vary over a wide range. In the determination

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of atomic weights, an effort is made to keep the error below 1 part in 104-105. in most analytical work, the allowable error lies in the range 1-10 parts per 1000 for components comprising more than 1% of the sample. As a rule, analyses should not be made with a precision greater than required. Up to a point, precision is a function of time, labor, and overall cost (Youden 1959).

The precision of an analytical result depends on the least exact method used in obtaining the result. In expressing the result, the number of figures given should be such that the next to the last figure is certain and the last figure is highly probable yet not certain. Thus 10% and 10.00% denote widely varying precision (Paech 1956). The following is an example of how an average result computed from several determinations should be expressed. Assume the moisture content of sugar is determined in triplicate, and the following results are obtained: 1.032, 1.046, and 1.036%. The average is 1.038%. However, because the difference between 1.032 and 1.046 is larger than 0.010, the results should not be expressed with more than two figures after the decimal point. Thus, the average result should be reported as 1.04% (not 1.038%), indicating that the first figure after the decimal point is certain, and the second one is probable but uncertain.

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The results of weighing, buret reading, and instrumental (including automatic) reading have limitations. Replication of analyses eliminates some the errors resulting from sampling, from heterogeneity of sampled material, and from indeterminate —accidental or random—errors in the assay. Although repetition of an assay generally increases the precision of the analysis, it cannot improve its specificity and accuracy. If, however, reasonable specificity and accuracy have been established, the precision of the assay is an important criterion of its reliability.

Sensitivity can be increased in tow ways: (1) by increasing the response per unit of analyzed substance (e.g., in colorimetric assays by the use of color reagents that have a high specific absorbance; in gravimetric determinations by the use of organic reagents with a high molecular weight) and (2) by improving the discriminatory power of the instrument or operator (e.g., in gravimetry by using a microbalance; in spectrophotometry by using a photomultiplier with a

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high magnifying power) (Anastassiadis and Common 1968). According to Horwitz (1982, 1983), the important components of

reliability, which are listed in their order of importance for most purposes in food analyses, are as follows:

1.Reproducibility—total between –laboratory precision 2.Repeatability—within-laboratory precision 3.Systematic error or bias—deviation from the “true” value 4.Specificity—ability to measure what is intended to be measured 5.Limit of reliable measurement—the smallest increment that can bemeasured with a statistical degree of confidence

Typical analytical systematic errors (biases) are plotted in Fig.4.2.Detection and determination of errors were described and discussed in detail by Cardone. Tolerances and errors are depicted

in Fig.4.3, in which the tolerance limits for the measured property are given by Lp and Cm indicates the uncertainty in the

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measurement. The values of Lp and Cm include estimates of the bounds for systematic errors or biases (B) and estimates of random errors (s, the estimate of standard deviation). Cm should be less than Lp. The confidence limits for , the mean of replicate

measurements, are

where is the so-called Student factor.

For regulatory purposes, reliability is paramount and reproducibility is the critical component (Horwitz 1982).The between-laboratory

coefficient of variation CV is represented by

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Where C is the concentration expressed as powers of 10(e.g., 1ppm, or 10-6, C=-6).The value of CV doubles for each decrease in concentration of two orders of magnitude. The between-laboratory coefficient of variation at 1 ppm is 16%(24).The within-laboratory CV should be one-half to two-thirds of the between-laboratory CV. The interlaboratory coefficient of variation as a function of concentration is illustrated in Table 4.5 and Fig.4.4.the largest contributors to experimental errors in instrumental methods are systematic errors(Horwitz 1984),which are difficult to measure without interlaboratory comparisons. They can be reduced by incorporating reference physical constants and certified standards.

The precision characteristics of 18 analytical methods for trace elements subjected to inter laboratory collaborative studies over the last 10 years by the Association of Official Analytical Chemists were examined by Boyer etal. (1985).Removal of outliers and statistical calculations were standardized by the use of a computer program.

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Most of the studies, which represented a variety of analytes matrices and measurement techniques over a range of concentrations of 100g/kg to 10µg/kg, were distributed about a

curve defined by the equation.

where RSDx is the among-laboratory standard deviation and C the concentration expressed as a decimal fraction (e.g., 1 ppm = 10-6), irrespective of analyte, matrix, or measurement technique. The within-laboratory relative standard deviation RSD0 was usually one-half to one-third RSDx. Positive deviations from this curve with decreasing concentration could be explained by heterogeneity of the material, free choice of analytical method, or concentrations below the limit of determination. The presence of more than 20% outlying laboratory results or RSDx degenerating faster than the “moral” rate

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with decreasing concentration was taken by the authors to indicate that a particular method is inapplicable at or below the level generating the imprecise data.

Optimizing chemical laboratory performance was the subject of a symposium organized by the Association of Official Analytical Chemists (Garfield et al.1980).The symposium covered a wide range of topics including design, criteria, and maintenance of quality assurance programs; reference standards; maintenance of records; and government regulations as they relate to good manufacturing practices and good laboratory practices(Piggott,1986;Hubbard 1990).Reliability measures in collaborative tests was discussed by Karpinski (1989).The author presented procedures for calculating confidence intervals and operating characteristic curves for acceptance criteria based on repeatability and reproducibility estimates. Comparisons of the reliability of estimates were provided for various numbers of collaborators. With a small number of collaborators, the estimates of reproducibility are not reliable and decisions regarding acceptability of a method are heavily based on the method’s repeatability rather than the property of most interest, namely, the reproducibility of the method. Wagstaffe (1989)

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discussed errors in analytical methods and the use of intercomparisons to locate sources of error and how to improve accuracy in food analyses. According to the author, although most analytical chemists achieve a good level of precision, relatively few evaluate maximum possible errors in their results. This is evident from the wide range of values often seen in interlaboratory trials. This problem arises largely because, unlike precision, accuracy is difficult to achieve and, within an isolated laboratory, often impossible to demonstrate. Certified Reference Materials (CRMs) provide an effective and economic means of investigating and controlling accuracy. Reference values (certification) are generally assigned to CRMs on the basis of agreement of independent methods. For many difficult analyses, certification cannot be achieved until the major sources of error have been identified and reduced. A systematic approach has been developed, which involves a series of preliminary studies, each designed to investigate specific steps in the analysis (e.g., calibration, extraction, clean-up, and end method). This procedure often leads to

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considerable improvements in the application of established methods and even to the development of new ones. The approach was illustrated with reference to recent studies in CRMs development for aflatoxin M1 in milk powder, aflatoxin B1 in peanut meal, deoxynivalenol in corn and wheat, and polycyclic aromatic hydrocarbons in kale and coconut oil.

The significance of reference material for improving the quality of nutritional composition data for foods was presented in a lecture by Southgate (1987). The main features of a quality assurance program must include adequate training; supervision and motivation of staff; proper organization of record keeping; adequate sampling to ensure that the samples are representative; preservation of composition during storage and exclusion of contamination; selection reliable analytical methods; and judicious evaluation of results. Major factor in selection of reference materials are variety of food matrices, from and distribution of nutrients in foods, species of nutrients (types and range of separation), and means of protecting labile nutrients. The reference materials should include major components (“proximate constituents”-water, protein, fat, and carbohydrates), inorganic constituents (major: Na, K, Ca, Mg, P, and Cl; minor: Cu, Mn,

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Cr, I, F, and Co; and Co; and boundary: Fe and Zn), and vitamins. Peeler et al. (1989) examined the available collaborative studies for standard methods of analysis for various constituents of milk and milk products in an attempt to assign specific repeatability and reproducibility precision parameters to these methods. The collaborative assays for the primary constituents (moisture/solids, fat, protein), the nutritionally important elements (calcium, sodium, potassium, phosphorus), and miscellaneous analytes/physical constants (ash, lactose, salt, freezing point) produced different estimates of the precision estimates from collaborative studies was given by the reproducibility relative standard deviation, RSDR, which is relatively constant within a product and permits comparisons across products. Horwitz et al. (1990) studied the precision parameters of methods of analysis required for nutrition labeling, with regard to major nutrients. The precision data are best summarized as a median or average parameter and the interval containing the centermost 90% of reported values. The precision of methods of analysis can be expressed as a function of concentration

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only, independent of analyte, matrix, and method. The average RSDR value from each collaborative data set can be used as the numerator in a ratio containing, as the numerator in a ratio containing, as the denominator, the value calculated from the Horwitz equation:

where C is the concentration as a decimal fraction. A series of ratios consistently above 1, and especially above 2, probably indicates that a method is unacceptable with respect to precision.

By this criterion, only the protein (Kjeldahl) determination is acceptable with a 90% interval for RSDR of 1-3% at C values above about 0.01(1g/100g). Fat, moisture/solids, and ash are acceptable down to limiting concentrations in the region of 1-5g/100g, if a test portion large enough to provide at least 50mg of weighable

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residue or volatiles is specified. Measurements of individual carbohydrates and fiber-related analytes have unexpectedly poor precisions among laboratories. The variability, although high, may still be suitable for nutrition labeling.

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