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Reporting Results and Reliability of Analyses
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introduce
Reporting Results
Reliability of Analyses
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Reporting Results and Reliability of Analyses
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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
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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.
%Y 
%Y  100
(100  %loss OD )
Reporting Results
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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:
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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 airdried 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.
Reliability of Analyses
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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
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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 110 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 onehalf 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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