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Laboratories typically focus on percent recovery to compare data.
How do you compare two analytes using percent recovery to
determine relative performance? How do you compare two
laboratories across a broad range of analytes? Percent recovery
is not an appropriate measure of performance across different analytes.
We will discuss this issue with examples from Trace Metals using Cadmium
and Chromium. Cadmium with an assigned value of 142, mean of 141, and Standard
Deviation of 6.97. Chromium with an assigned value 779, mean of 780 and a
standard deviation of 33.5. Both these analytes should have approximately
100% percent recovery based on EPA Methods. Is it true then that 90%
recovery alone would indicate equal performance on these two analytes?
The graphs below begin to shed light on the problem of using this measure
against two separate analytes.
Why ZScores
As you can see from the graphs above 90% recovery for Cadmium puts you almost
one and a half standard deviations away from the mean recovery. While 90%
recovery of Chromium puts you less than 0.3 standard deviations away from
the mean recovery. It should begin to become clear that 90% recovery is not
an accurate measure of how well you performed on an analyte. Now that we
are taking the variability of the sample into account we see that 90% recovery
of Chromium is much closer to expected performance than 90% recovery of Cadmium.
The problem with comparing these two analytes lies in the fact that although
both distributions expect 100% recovery they have very different standard
deviations. Using both percent recovery and standard deviation changes our
perception of their performance by showing their actual relative performance.
Now that the benefits of relative performance over simple pass/fails and
percent recoveries are understood we’ll look at how its done.
Calculating ZScores
The method of comparing desperate data using both a normalized mean and
standard deviation is referred to as a ZScore. This internationally
recognized standardize score is calculated by comparing how far a
lab is from the normalized mean expressed in terms of standard deviation units.
ZScore: (Result - Mean) / Standard Deviation
Cadmium ZScore: (126.9 - 131) / 6.97 or -0.59
Chromium ZScore: (702 - 780) / 33.5 or -2.33
The negative expressed in the ZScores above denote performance below
the mean. If we had 110% Recovery for Cadmium our ZScore would have
been 1.43 showing performance greater than the mean. A negative or
positive ZScore shows whether a result was above or below the mean
and gives no indication of performance. A -0.2 ZScore is similiar
to a 0.2 ZScore. The difference is one is below and one above the
mean respectively.
Advantage of ZScores
ZScores provide a way to standardize performance of
different metrics. The example works not because both analytes
have the same expected mean with different standard deviations
but because the two data sets where normalized. Each ZScore comes
from a distribution with the same mean (zero) and the same
standard deviation (one). We can therefore compare relative
performance of all analytes using this relative performance.
While percent recovery provides a great deal of information about
an analytes performance we can now answer resoundingly that it can
not be used to compare different analytes relative performance. APG
is proud to be the only NVLAP certified provider that provides its
customers with their ZScores on every report.
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