FOOD ANALYSIS : DATA QUALITY
Repeats agree with each other
and with the true value
Repeats agree with each other
but sit away from the true value
Repeats average to the true value
but scatter widely
Repeats scatter
and sit away from the true value
Precise values agree with each other. Accurate values agree with a true value.
Figure 1: The four combinations of accuracy and precision. A laboratory aims for both at once.
Introduction
Accuracy and precision are the two words a laboratory uses to judge its results, and they mean different things. Accuracy is how close a measured value is to the true or accepted value. Precision is how close repeated measurements are to each other. A set of results can be precise without being accurate: the repeats agree with each other but all sit away from the true value. It can also be accurate on average without being precise: the repeats scatter widely but their mean lands on the true value. Good laboratory work needs both.
Quick comparison
Table 1: Accuracy compared with precision
| Aspect | Accuracy | Precision |
|---|---|---|
| What it means | Closeness to the true or accepted value | Closeness of repeated measurements to each other |
| Needs | A true or accepted value to compare against | Repeated tests on the same sample |
| Judged by | Error: the gap between the result and the true value | Spread: the standard deviation of the repeats |
| Checked with | A standard or reference sample run with the batch | Duplicates: if two results differ by more than the method allows, run the test again |
| Harmed by | Systematic error, such as a wrong calibration or a faulty method | Random variation, such as uneven sampling or unsteady technique |
| Fixed by | Calibration, blanks, and checking against a standard | Steady technique, good sampling, and repeat testing |
| Example | A moisture test that reads 12.0 percent when the true value is 12.0 percent | Three moisture repeats of 12.0, 12.1, and 12.0 percent |
| Reporting | A test accurate to 0.1 percent is reported to one decimal place, not three | Extra digits pretend to a precision the test does not have |
Scientific explanation
Definition
Accuracy: how closely a measurement aligns with a correct or accepted value. Precision: how closely a measurement matches the same measurement when repeated. Mean: the average of the repeats. Standard deviation: a measure of how much the repeats spread around the mean. A small spread means the work was steady, and a large spread means something varied.
Working principle
Accuracy is judged against a known value. The analyst runs a standard or a reference sample with the batch, and if the standard reads wrong, the whole batch is suspect. A blank is run and subtracted, so the reagents do not add to the result. Precision is judged from repeats. Statistics turn a set of repeated results into a judgement: the mean is the average of the repeats, and the standard deviation measures how much the repeats spread around the mean. When a set of measurements is precise but not accurate, the error is usually systematic, and it comes from faulty instrumentation or faulty technique.
Apparatus
Both use the same laboratory instruments as the test itself. Accuracy needs, in addition, a standard or reference sample of known value and a blank. Precision needs no extra instrument: it needs the test run more than once on the same sample.
Measurement procedure
Run the test in duplicate, and if the two results differ by more than the method allows, run it again. Run a blank and subtract it. Run a standard or a reference sample with the batch, and if the standard reads wrong, the whole batch is suspect. Check the proximate sum: the parts should add to near 100. Report the result with the right number of figures: a test accurate to 0.1 percent is reported to one decimal place, not to three, because the extra digits pretend to a precision the test does not have.
Factors affecting readings
Accuracy: a wrong calibration, a missed blank, a wrong factor, or a method used on the wrong food all push the result away from the true value. Precision: uneven sampling, unsteady technique, and changing conditions between repeats all widen the spread. A report of 12.47 percent from a test that is only good to 0.1 is not more accurate: it is less honest, because a reader who sees 12.47 percent believes the result is known to a hundredth, when the test only supports a tenth.
Formulas and calculations
Percent error = the absolute difference between the measured value and the true value, divided by the true value, times 100. Mean = the sum of the repeats divided by the number of repeats. The standard deviation measures the spread of the repeats around the mean.
Worked example, using the milk total solids value from the FTN notes: the accepted value for a milk is 12.5 percent total solids. A laboratory reads 12.4, 12.5, and 12.6 percent. The mean is 12.5 percent, so the percent error of the mean is 0, and the spread is small: the work is accurate and precise. A second laboratory reads 11.4, 11.5, and 11.6 percent. The repeats agree with each other, so the work is precise, but the mean is 11.5 percent, and the percent error is 1.0 divided by 12.5, times 100 = 8.0 percent: the work is precise but not accurate, and the cause is usually a systematic error such as a wrong calibration.
Industrial applications
- Quality control laboratories run duplicates on every batch, and a gap wider than the method allows sends the test back for a repeat.
- Reference samples are run with each batch, so a wrong standard reading warns the laboratory before results go out.
- Trade disputes are settled by accuracy: the laboratory whose result sits closest to the accepted value wins the argument.
- Method checks compare a new fast method against the reference method on the same samples, judging both its accuracy and its precision.
Advantages and limitations
Accuracy: it is the quality that makes a result true and useful for payment, safety, and trade. Its limit is that it cannot be judged from repeats alone: without a true value to compare against, an accurate-looking set of repeats can all be wrong together.
Precision: it is easy to judge from repeats, and it shows whether the work is steady. Its limit is that it says nothing about truth: precise repeats can all sit away from the true value, and a precise but wrong result is still wrong.
FAQ
Question: Can results be precise but not accurate?
Yes. The repeats agree with each other but all sit away from the true value. The cause is usually a systematic error, such as a faulty calibration or faulty technique.
Question: Can results be accurate but not precise?
Yes, on average. The repeats scatter widely but their mean lands on the true value. The work is not steady, and single results cannot be trusted.
Question: Two duplicate moisture results are 12.0 and 12.9 percent. What should the analyst do?
Run the test again. The gap is too large for a method that should repeat within a few tenths, so one of the two results is wrong, and reporting their average would hide the problem.
Question: Why is reporting too many decimal places dishonest rather than merely untidy?
Because the extra digits claim a precision the test does not have. A reader who sees 12.47 percent believes the result is known to a hundredth, when the test only supports a tenth.
Question: How does a laboratory check accuracy every day?
It runs a standard or a reference sample with the batch. If the standard reads wrong, the whole batch is suspect.
References and further reading
- FTN Food Analysis, Unit 7: Acidity, pH, safety testing and analytical data (notes on disk): mean, standard deviation, duplicates, blanks, standards, significant figures, worked example 12.47 percent.
- Skoog, D. A., West, D. M., Holler, F. J., and Crouch, S. R., Fundamentals of Analytical Chemistry: accuracy, precision, percent error, standard deviation (consulted through Google Books).
- Nielsen, S. S., Food Analysis, Springer: analytical data and quality checks (consulted through Google Books).
