tected may be caused by subsampling error
the samples is of concern, and high variability in
(sample was not homogeneous and the splits ac-
sample results caused by poor precision rather
tually contained different concentrations of explo-
than variability in the true concentration is well
sives), or differences in extraction efficiency (shak-
handled by these methods.
ing with acetone versus ultrasonication with aceto-
nitrile), rather than the analytical methods, which
Precision and bias tests for measurements over
may also produce different results. However, if a
large value ranges
group of acetone "extracts" are analyzed by two
When the concentrations of explosives cover a
different methods, the subsampling and extraction
large range of values, regression methods for as-
errors are minimized and any significant dif-
sessing precision and accuracy become appropri-
ferences should be from the analytical methods.
ate. Regression analysis is useful because it allows
characterization of nonconstant precision and bias
effects and because the analysis used to obtain
Precision and bias tests for measurements
prediction intervals for new measurements (e.g.,
of relatively homogeneous material
When multiple splits of well-homogenized soil
the results of an on-site method) can be used to
samples are analyzed using different analytical
predict the concentration if the samples were ana-
methods, statistical procedures described in
lyzed by a reference method.
Grubbs (1973), Blackwood and Bradley (1991), and
In a regression analysis, the less precise on-site
Christensen and Blackwood (1993) may be used
method is generally treated as the dependent vari-
to compare the precision and bias of the methods.
able and the more precise reference analytical
Grubbs (1973) describes a statistical approach ap-
method (e.g., SW-846 Method 8330) as the inde-
propriate for comparing the precision of two meth-
pendent variable. To the extent that the relation-
ods that takes into account the high correlation
ship is linear and the slope differs from a value of
between the measurements from each method. An
1.0, there is an indication of a constant relative bias
advantage of Grubbs' approach is that it provides
in the on-site method (i.e., the two methods differ
unbiased estimates of each method's precision by
by a fixed percentage). Bias should be expected if
partitioning the variance of the measurement re-
on-site methods based on wet-weight contaminant
sults into its component parts (e.g., variance
levels are compared to laboratory methods based
caused by subsampling and by the analytical
on the dry weight of soil samples. Similarly, an
method). Blackwood and Bradley (1991) extend
intercept value significantly different from zero
Grubbs' approach to a simultaneous test for equal
indicates a constant absolute bias (i.e., the two
precision and bias of two methods. Christensen
methods differ by a fixed absolute quantity). There
and Blackwood (1993) provide similar tests for
may, of course, be both fixed and relative bias com-
evaluating more than two methods.
ponents present.
For comparisons involving bias alone, t-tests or
When uncertainty is associated with the con-
analysis of variance may be performed. For com-
centration of an explosive as measured by the ref-
paring two methods, paired t-tests are appropri-
erence method, standard least squares regression
ate for assessing relative bias (assuming normal-
analysis can produce misleading results. Standard
ity of the data, otherwise data transformations to
least squares regression assumes that the indepen-
achieve normality must be applied, or nonpara-
dent variable values are known exactly as in stan-
metric tests used). A paired t-test can be used to
dard reference material. When the on-site method
test whether the concentration as determined by
results contain appreciable error compared to the
an on-site method is significantly different from
reference method, regression and variability esti-
Method 8330 or any other reference method. For
mates are biased. This is known as an errors-in-
comparing multiple methods, a randomized com-
variables problem.
plete block analysis of variance can be used, where
Because of the errors-in-variables problem, the
the methods are the treatments and each set of split
slope coefficient in the regression of the on-site
samples constitutes a block.
data on the reference data will generally be biased
These tests are best applied when the concen-
low. Hence a standard regression test to determine
trations of explosives are all of approximately the
whether the slope is significantly different from 1
same magnitude. As the variability in the sample
can reject the null hypothesis even when there is
concentration increases, the capability of these
in fact no difference in the true bias of the two
tests for detecting differences in precision or bias
methods. A similar argument applies to tests of
decreases. The variability in the true quantities in
the intercept value being equal to zero.
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