What are accuracy and precision …
… are they not the same?
There is still misuse and misunderstanding of the terms accuracy and precision in relation to geochemical analyses and measurements. Often both terms appear to be interchangeable.
An internet search even produced a definition of ‘accuracy’ using “being correct or precise”.
It is of paramount importance to understand the meanings and differences of these two terms for a meaningful description of (geo-) chemical analyses/measurements and data in a scientific way.
Accuracy
Accuracy describes how close a measurement/result comes to the true value.
Determining the accuracy of a measurement usually requires calibration of the analytical instrument with reference materials of known compositions.
Precision
Precision describes the repeatability or reproducibility of multiple measurements/results. It is usually described by the standard deviation, standard error, or confidence interval (see below).
Let’s visualize this
A popular way to explain the difference between accuracy and precision is the analogue of hitting a target.
Figure 1: Low accuracy and low precision.
Figure 1:
The target has been hit, but the hits are widely scattered, which means the hits are of low accuracy and low precision.
Figure 2: Low accuracy, but high precision.
Figure 2:
This time, the hits are clustered close together, but not in the center. The target has been hit with high precision, but with low accuracy (i.e., still missing the bull’s-eye).
Figure 3: High accuracy, but low precision.
Figure 3:
The hits are clustered, but close to the center; so the target is hit with high accuracy, but with low precision.
Figure 4: High accuracy and high precision.
Figure 4:
The hits cluster closely in the center. The target center has been hit with high accuracy and high precision.
Why is it important?
It is kind of self-explanatory why we are aiming to achieve high accuracy and precision when analyzing rock samples for their geochemical compositions.
We need to have an idea about how good and reliable the data are before placing any interpretation on them.
Interpretations of data with low precision lead to spurious results. This is particularly true for chemostratigraphic interpretations. Let’s assume a correlation between two sections (e.g., wells) is required. With low precision data, it is even unclear if we compare (correlate) like with like (the proverbial comparing apples with oranges).
Data with high precision, but low accuracy may still lead to reasonable basic interpretations, as long as the deviation is constant (and maybe can even be corrected). These data can at least be interpreted in terms of relative variations.
Advanced interpretations and mineral and/or rock properties modeling are only possible with with precision and high accuracy data.
How can we measure accuracy and precision?
1. How to calculate accuracy?
Accuracy can be expressed as a percentage of error or accuracy in relation to the true value.
where Vt is the true values, and Vm the measured value.
For instance, Vt = 10, Vm = 9.8, thus percent error = 2%, and percent accuracy = 98%.
Accuracy can be expressed as percent error and/or percent accuracy. You need the true value, e.g., the elemental concentration from a standard reference material (SRM), to calculate these values.
2. How to calculate precision?
A way to express the precision is to calculate the standard deviation. The standard deviation is a statistical measure of the precision for a series of repeated measurements; in other words, the standard deviation measures how widely the data points are spread.
Most likely, you will have access to Microsoft Excel (or any other spreadsheet software with basic statistical functions). Older versions of Excel use the STDEV function, while newer versions use the STDEV.S function; the results are the same.
where N is the number of measurements, Xi is each individual measurement, and ẋ is the means (average) of all measurements.
For example, if all measurements would result in the same number, the numbers would have a standard deviation of 0 (zero). The lower the standard deviation the closer the measurements are to the mean, the better the precision.