# Calculating Precision

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Radon and working level measurements, like all measurements, usually do not produce exactly the same results, even for co-located measurements. It is therefore critical to understand, document, and monitor the variability, or precision, of the measurements. This knowledge and proper documentation will allow you to characterize precision error to clients. Furthermore, the continual monitoring of precision provides a check on every aspect of the measurement system.

The objective of performing simultaneous or duplicate measurements is to assess the precision error of the measurement method, or how well two side-by-side measurements agree. This precision error is the “random” component of error (as opposed to the calibration error, which is systematic). The precision error, or the degree of disagreement between duplicates, can be composed of many factors. These include the error caused by the random nature of counting radioactive decay, slight differences between detector construction (for example, small differences in the amount of carbon in activated carbon detectors), and differences in handling of detectors (for example, differences in accuracy of the weighing process, and variations of analysis among detectors).

How to Calculate Precision

There are a variety of ways to quantitatively assess the precision error based on duplicate measurements. It is first necessary to understand that precision is characterized by a distribution; that is, your side-by-side measurements will exhibit a range of differences. There is some chance that any level of disagreement will be encountered, due merely to the statistical fluctuations of counting radioactive decays. The probability of encountering a very large difference between duplicates is smaller than the chance of observing a small difference similar to those that are routinely observed. It is important to recognize that a few high precision errors do not necessarily mean that the measurement system is flawed.

The precision of a series of measurements can also be identified as the standard deviation (STD) of those measurements. The standard deviation measures the statistical range from the average measurement.  Sometimes precision can be determined by simply by looking at how close the measurements are grouped together.

For example, compare the 2 groups of measurements:

Regardless of what the target value may be, group 1 is clearly more precise.

There are other common equations in assessing precision.  The EPA Radon Measurement Quality Assurance report should be referenced for full explanation.  In summary, the following are cited:

Coefficient of Variation (COV)

COV is calculated by dividing standard deviation by the mean.

Relative Percent Difference (RPD)

RPD is determined by calculating the difference between 2 measurements, divided by the mean.

For example, if a person aims a rifle at the “bull’s-eye” on a target and consistently hits the outermost ring at 2 o’clock position, the precision is excellent, but the accuracy is poor because of large bias. When the rifle bullets are within the bull’s-eye every time, the rifle is both precise and unbiased; hence there is good accuracy. Finally, the scattered holes at the 7 o’clock position have both a poor bias and a poor precision, resulting in a very poor accuracy.