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Precision and Accuracy of a Measurement Instrument

This concept of random and systematic errors is related to the precision and accuracy of measurements. Precision characterizes the system's probability of providing the same result every time a sample is measured (related to random error). Accuracy characterizes the system's ability to provide a mean close to the true value when a sample is measured many times (related to systematic error).

A simple example of this is shown in Figure 9. The red "x" marks show a high precision but low accuracy measurement. The datapoints are all very close to each other. However, if we calculated the mean of these measurements, it would be fairly far from the true value (the center of the rings). If we make another measurement, we would expect it to also be close to the previous measurements. The blue "+" marks have a low precision but a high accuracy since the mean of these measurements will be very close to the true value even though the measurement points have a large spread in values. Thus, if we made another measurement we would not expect it to be close to any particular previously measured value, but if we made many measurements then the experimental mean would likely be a good estimate of the true value.

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Figure 9. Example showing the difference between a high accuracy measurement (denoted by the blue "+" marks) and a high precision measurement (denoted by the red "x" marks) where the center of the target is the true value.

We can determine the precision of a measurement instrument by making repeated measurements of the same sample and calculating the standard deviation of those measurements. However, we will not be able to correct any single measurement due to a low precision instrument. Simply stated, the effects of random uncertainties can be reduced by repeated measurement, but it is not possible to correct for random errors.

We can determine the accuracy of a measurement instrument by comparing the experimental mean of a large number of measurements of a sample for which we know the "true value" of the characteristic of the sample. A sample for which we know the "true value" would be our calibration standard (i.e., a sample that is very well characterized or built to specific specifications). We may also need to characterize the accuracy of the measurement instrument by observing historical trends in the distribution of measured values for the calibration standard (this allows for determining the systematic error expected from environmental effects, etc.). The effects of systematic uncertainties cannot be reduced by repeated measurements. The cause of systematic errors may be known or unknown. If both the cause and the value of a systematic error are known, it can be corrected for by "subtracting" the known deviation. However, there will still remain a systematic uncertainty component associated with this correction.

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