# Accuracy and precision

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**Accuracy**, in science, engineering, industry and statistics, is the degree of conformity of a measured/calculated quantity to its actual (true) value. **Precision** (also called reproducibility or repeatability) is the degree to which further measurements or calculations will show the same or similar results.

The results of a measurement or calculation can be accurate but not precise, precise but not accurate, neither, or both; if a result is both accurate and precise, it is called *valid*.

The related terms in surveying are **error** (random variability in research) and **bias** (nonrandom or directed effects caused by a factor or factors unrelated by the independent variable).

## The target analogy

Image:Accuracy and precision-highaccuracylowprecision.gifImage:Accuracy and precision-highprecisionlowaccuracy.gif

By far the most common analogy used to explain the concept is the target comparison.

Repeated measurements are compared to arrows that are fired at a target. Accuracy describes the closeness of arrows to the bullseye at the target center. Arrows that strike closer to the bullseye are considered more accurate. The closer a system's measurements to the accepted value, the more accurate the system is considered to be.

To continue the analogy, if a large number of arrows are fired, precision would be the size of the arrow cluster. (When only one arrow is fired, precision is the size of the cluster one *would* expect if this was repeated many times under the same conditions.) When all arrows are grouped tightly together, the cluster is considered precise since they all struck close to the same spot, if not necessarily near the bullseye. The measurements are precise, though not necessarily accurate.

However, it is *not* possible to reliably achieve accuracy in individual measurements without precision - if the arrows are not grouped close to one another, they cannot all be close to the bullseye. (Their *average* position might be an accurate estimation of the bullseye, but the individual arrows are inaccurate.)

Accuracy is the degree of veracity while precision is the degree of reproducibility.

## Quantifying accuracy and precision

Ideally a measurement device is both accurate and precise, with measurements all close to and tightly clustered around the known value.

The accuracy and precision of a measurement process is usually established by repeatedly measuring some traceable reference standard. Such standards are defined in the International System of Units and maintained by national standards organizations such as the National Institute of Standards and Technology.

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Precision is usually characterised in terms of the standard deviation of the measurements, sometimes called the measurement process's standard error.

With regard to accuracy we can distinguish:

- the difference between the mean of the measurements and the reference value, the bias. Establishing and correcting for bias is necessary for calibration.
- the combined effect of that and precision

A common convention in science and engineering is to express accuracy and/or precision implicitly by means of significant figures. Here, when not explicitly stated, the margin of error is understood to be one-half the value of the last significant place. For instance, a recording of '8430 m' would imply a margin of error of 5 m (the last significant place is the tens place), while '8000 m' would imply a margin of 500 m. To indicate a more accurate measurement that just happens to lie near a round number, one would use scientific notation: '8.000 x 10^3 m' indicates a margin of 0.5 m. However, reliance on this convention can lead to false precision errors when accepting data from sources that do not obey it.

Looking at this in another way, a value of 8 would mean that the measurement has been made with a precision of '1' (the measuring instrument was able to measure only up to 1's place) whereas a value of 8.0 (though mathematically equal to 8) would mean that the value at the first decimal place was measured and was found to be zero. (The measuring instrument was able to measure the first decimal place.) The second value is more precise. Neither of the measured values may be accurate (the actual value could be 9.5 but measured inaccurately as 8 in both instances).

Precision is sometimes stratified into:

*Repeatability*- the variation arising when all efforts are made to keep conditions constant by using the same instrument and operator, and repeating during a short time period; and*Reproducibility*- the variation arising using the same measurement process among different instruments and operators, and over longer time periods.de:Genauigkeit