Accuracy Explained

In our field of work, we come across many research papers where the concept of accuracy is discussed – be it the accuracy of a measurement system, or the assessed clinical accuracy of targeting a specific point in space. Unfortunately, there is inconsistency as to what is precisely meant by “accuracy”, and this article will make a brief attempt at explaining this.

Trueness and Precision

Accuracy, as per ISO 5725:1994, is defined as: 'closeness of agreement between a test result and the accepted reference value', and can be broken down into 'trueness' and 'precision'.

Trueness is defined as:

• The closeness of agreement between the average value obtained from a larger series of test results and an accepted reference value.
• It represents measurement bias or systematic error.

Trueness reflects the level of 'correctness' of a measurement or how close the measurement is to the true value. A repeated number of measurements should have (zero-mean) random errors and eventually cancel each other, leaving trueness.

Precision is defined as:

• The closeness of agreement between independent test results obtained under stipulated conditions.
• It represents random error, variability, repeatability, and reproducibility.

Precision describes the spread of measurement values. It does not say whether the average value is correct or not, but does say how much random error there is in the system.

Accuracy is best represented in both trueness (or mean error, ) and precision (or Standard Deviation, ). One measure of both is RMS Error ~ .

Mean Error vs. RMS Error

Looking at mean error alone ignores the spread of the data and is only an average of the error. The RMS error calculation includes the standard deviation of the data and is it tells more of a story as it is sensitive to large errors.

Maximum Error vs. 95% Confidence Interval

Often, the statistic of ‘maximum error’ is used. However, this is a very sensitive statistic and an outlying data point can severely skew the statistic. For even a semi-robust maximum error estimate, a larger data set is required.

A better measure is the “95% Confidence Interval”. This is the range in which 95% of all measurements fall and as such, not affected by a single bad measurement. It is a robust statistic that is more indicative of the results a user can expect from the system.

Summary

Though this article was brief, it has demonstrated the usefulness of using statistics of RMS Error and 95% Confidence Interval over the often seen Mean and Maximum Error statistic. One thing to keep in mind, regardless of the statistics used, accuracy is always measured relative to a protocol. When comparing apples to apples, make sure the protocols are equivalent.

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