4d01
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`Getting Started in HPLC
`Section 4D. Precision and Accuracy
`
`People often confuse "precision" with
`"accuracy". Both words suggest that we are
`doing careful work and getting the right answers
`in quantitative analysis. But precision is not the
`same as accuracy, and it is important to know
`what we are talking about. Accuracy means
`getting an answer that is correct. Precision
`means being able to get the same answer for a
`particular sample every time, when we repeat
`an analysis on that sample.
`
`Let's use an example from the LC lab. Suppose we weigh out 500 mg of aspirin and
`dissolve it in a 100 mL flask. The concentration of aspirin in our sample will then be :
`
`(quantity) / (volume) = (500 mg)/(l00 mL)
`
`= 5.00 mg/mL
`
`of aspirin.
`
`Now let's send 25 mL of this solution to three different laboratories: lab A, lab B and lab
`C. Each lab then analyzes the sample for aspirin (by means of HPLC) 6 times and
`reports the results to us as shown below right (Correct Concentration = 5.00 mg/mL)
`
`The results for lab A all fall quite close to each
`other: 5.40-5.45 mg/mL aspirin. When replicate
`analyses on a sample agree closely, as in this
`example, we say that the assay is precise. That
`is, a precise analysis is a reproducible analysis.
`However we also see that these values (5.40-
`5.45) are not very close to the true value of 5.00
`mg/mL. The average value (5.42 mg/mL) is
`about 8% too high.
`
`Now consider the results for lab B. These range
`from 4.80 to 5.18 mg/mL. When we see values
`that scatter this much, we say that the analysis
`is not very precise or is imprecise. However if
`we average these values for lab B, we see that
`the average value (5.06 mg/mL) is pretty close
`to the true value of 5.00 mg/mL. So even
`though lab B does not report precise values, the
`
`LAB C
`LAB B
`LAB A
`5.03
`5.18
`5.45
`4.98
`4.80
`5.40
`5.00
`5.20
`5.42
`5.03
`5.06
`5.43
`4.98
`5.15
`5.40
`5.03
`4.98
`5.41
`PRECISE
`IMPRECISE
`PRECISE
`INACCURATE ACCURATE ACCURATE
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`values reported are closer to the true value than
`for lab A. We say that lab B is accurate - even if
`it is imprecise.
`
`Finally for lab C in the above example, we see that the values reported (4.98-5.03
`mg/mL) agree with each other quite well, and the average value (5.01 mg/mL) is also
`close to the correct value of 5.00. So lab C can be said to be both precise and accurate.
`
`Both accuracy and precision are important in HPLC analysis. However it is much easier
`to measure precision than it is to measure accuracy. We can easily rerun a sample
`several times and show that the results are reproducible or precise. It is often more
`difficult to know the exact concentration of some compound in a given sample -
`particularly a "real" sample that comes to us in some strange mixture. This often results
`in laboratories reporting answers that appear precise but are actually wrong
`(inaccurate). It is actually much more important that our answers be accurate than
`precise, although good accuracy also requires good precision. The bottom line is: if you
`have shown that your analysis is precise, don't assume that it is also accurate. Accuracy
`has to be demonstrated in a different way.
`
`While we are talking about precision - which is
`essential to good HPLC results - it is important
`to mention a common error in quantitative
`analysis. This is the practice of using too few
`decimals in recording results or carrying out
`calculations. Be sure to retain enough
`SIGNIFICANT FIGURES in all weights, volumes
`and calculations. Generally in LC analysis we
`want to have at least 4 significant figures in
`every number, and sometimes more. For
`example, if weighing out a sample, make sure
`that the sample weight after subtracting off the
`tare weight has at least 4 significant figures as
`shown at the right.
`
`CORRECT INCORRECT
`flask 124.3433 g
`124.34 g
`flask+sample 123.8877 g
`123.89 g
`sample
`0.4556 g
`0.45 g
`
`The most common measures of precision in chromatographic measurements are the
`standard deviation, the relative standard deviation, and the coefficient of variation.
`Detailed definition of these measures is outside the scope of this course; it can be found
`in any textbook on quantitative analysis or statistics. In practice, the values are
`computed automatically by the data system or a computer spreadsheet.
`
`Very briefly, the standard deviation is a measure of the amout of possible random error
`in a series of replicate measurements. For truly random errors, two-thirds of the values
`will lie within ±1 standard deviation of the mean, 95% of the values will lie within ±2
`standard deviations of the mean, and 99% of the the values will lie within ±3 standard
`deviations of the mean. The estimated standard deviation for a quantity is symbolized
`by a lower-case sigma (s).
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`The relative standard deviation is the standard deviation as a fraction of the mean value.
`Thus, if we measure a concentration of 9.52 mg/mL with a standard deviation of 0.110
`mg/mL, the relative standard deviation is:
`
`RSD = 0.1 10/ 9.52 = 0.0115
`
`In practice, this often expressed at the coefficient of variation (CV), sometimes also
`called "percent relative standard deviation" (%RSD). This is simply the relative standard
`deviation expressed as a percentage instead of as a decimal fraction. The CV for the
`example above is 1.15% (the percentage equivalent to the fraction 0.0115). To convert
`from RSD to CV, multiply the RSD by 100.
`
`We can now re-examine the results of the
`aspirin analysis at three different laboratories
`that we discussed near the top of the page. The
`mean, standard deviation, and CV give us a
`more meaninful picture of the laboratories'
`performance than the terms "precise" or
`"imprecise".
`
`For most purposes, HPLC methods are
`expected to have CV values on the order of 1%.
`Less precision may me acceptable in the case
`of extremely low-level samples or where a
`simple yes/no decision is required. The
`expected precision will usually be stated as part
`of the method specification.
`
`LAB A LAB B LAB C
`
`5.45
`5.40
`
`5.42
`
`5.43
`5.40
`
`5.18
`4.80
`
`5.20
`
`5.06
`5.15
`
`5.03
`4.98
`
`5.00
`
`5.03
`4.98
`
`5.03
`4.98
`5.41
`5.01
`5.06
`MEAN 5.42
`0.025
`0.15
`STD. DEV. 0.019
`CV 0.35% 4.6% 0.36%
`
`Mini-Quiz
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`Glossary
`
`-----
`
`Contents
`
`© 2000, LC Resources Inc. All rights reserved.
`Last revised: April 06, 2001.
`
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`9/30/2015
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`SteadyMed - Exhibit 1017 - Page 3