Reporting%20Results%20and%20Reliability%20of%20Analyses

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Reporting Results and Reliability of Analyses
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introduce
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Reporting Results
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Reliability of Analyses
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Reporting Results and Reliability of Analyses

• 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

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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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Reporting Results

• 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

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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
  6.25100/16 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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Reliability of Analyses

• 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

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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 (lt10), 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 indeterminateaccidental or
  randomerrors 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.Reproducibilitytotal between
  laboratory precision
• 2.Repeatabilitywithin-laboratory
  precision
• 3.Systematic error or biasdeviation from
  the true value
• 4.Specificityability to measure what is
  intended to be measured
• 5.Limit of reliable measurementthe
  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,1986Hubbard 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 methods 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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