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Article written by Audra Clark, Chemist, Analytical Products Group
Complete Article from Edition 11 APG eNewsletter
The importance of a good calibration cannot be emphasized enough.
Calibration is the key to accurate data. Without a sound calibration
your data is essentially useless. This article will review the fundamentals
of good calibration.
Calibration standards are known standards that are used to generate a
calibration curve. You must know two things about a material to use it
as a calibration standard – the identity of the material and the true
value or assay. A calibration curve demonstrates the relationship
between instrument response and concentration. This relationship is
usually linear. For any one response, there is only one corresponding
concentration.
The Importance of Slope
Most calibration curves are based on a linear relationship
that can be expressed using the equation for a straight line, y = mx + b.
In this equation, y is the instrument response, x is the concentration,
m represents the slope of the line, and b is the y-intercept. Most labs
use the correlation coefficient to make certain that a curve is linear.
However, slope is also an important variable. Take a look at the next
two examples.
Example One: Is this a good calibration?
Slope = 188.5391
Y-intercept = 8.8212
Correlation Coefficient = 0.9998
Example Two: Is this a good calibration?
Slope = 15.2147
Y-Intercept = 0.1721
Correlation Coefficient = 0.99999
Both correlation coefficients appear acceptable but look at what happens when the
curves are plotted on the same chart.
The calibration curve for Example 1 has a greater slope and is much more
sensitive. This makes it the better choice over Example 2. When comparing
calibration curves it is just as important to compare the slopes as it is
to make sure the correlation is sufficient.
Quality Control Standards
Now take a look at the following situation: A 1000 ppm Fe stock is
diluted 1:100 to create a 10 ppm stock. Then, this 10ppm stock is
diluted 1:2 and 1:10 to produce 5 ppm and 1 ppm stocks. If these three
standards, 1, 5, and 10 ppm, are then used to create a calibration
curve, the result is a one point curve. Consequently, the entire calibration
curve (though it may appear linear) is also incorrect if the first
dilution is incorrect for any reason. All
calibrations and especially those created by serial dilution should
be verified against an independent quality control standard.
Quality control standards verify that a calibration is correct
and are the key to defensible data. The following information is
required for a material to be used as a quality control
standard:
1. identity of the material
2. the true value of the material
3. a performance measure for the sample.
The performance measure is usually provided in the form of an
acceptance range. The calibration is satisfactory if the analysis result
for the quality control standard falls within the acceptance range. The
key to effectively using quality control standards is to bracket
the samples. The typical order for an analysis is similar to
the following:
1. Calibration Standards
2. First quality control sample
3. Samples 1 – 10
4. Second quality control sample
It is important to bracket every ten samples with quality control
standards because the first quality control standard verifies the
calibration curve and the second quality control standard verifies
that the sample data is valid. Both confirm the overall performance
of the analysis.
Calibration Verification
It is important to verify the following when verifying that
a calibration curve is acceptable:
- the correlation coefficient
- the slope (use the 95% confidence interval of the previous calibration’s slope to verify that no change has occurred)
- the quality control standards (should fall within a 99% confidence interval of the standard)
- the high end of the curve
- the low end of the curve
Evaluating the High and Low Ends of the Calibration Curve
We previously covered the first three checks and will now discuss how
to evaluate the high and low ends of a curve. To evaluate the high
end of a curve compare the slope of the entire line to the slope
between the top two points in the calibration. These slopes should
not vary by more than 5%. If they do, you may not be operating
within the linear range of the calibration curve. To evaluate the
low end of a curve, run replicate samples at each concentration in
the calibration and plot concentration versus relative standard
deviation (RSD) at each point. This produces a Horowitz Curve
and should have a characteristic shape as shown below. Adjust
your calibration range to include only points that have
an acceptable RSD.
Evaluation of the high end and low end of a calibration curve should
be completed during method development. Although checking the
correlation coefficient and slope will also be used in
developing a method, it is important to use these checks, as well
as quality control standards, on a routine basis to assure
the accuracy and defensibility of your analysis. Remember, your
data is only as good as your calibration.
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