Measurement precision

Measurement precision describes agreement among repeated indications or measured values obtained under stated conditions. It is commonly characterized using a standard deviation, variance or coefficient of variation, which describe the observed spread. Measurement repeatability is precision under a particular restricted set of conditions; intermediate measurement precision and measurement reproducibility concern other specified conditions.^[ref]

For an original balance example, take three repeat readings of a reference object: $100.100$, $100.080$ and $100.120\mathrm{g}$. Their arithmetic mean and sample standard deviation areSuppose the reference object's assigned mass is $100.000\mathrm{g}$ with standard uncertainty $0.002\mathrm{g}$. The observed mean differs from that reference by $0.100\mathrm{g}$, much more than the within-series scatter. These chosen readings therefore illustrate why close repeat readings do not establish agreement with a reference. They do not determine the true systematic offset from only three trials.

Measurement accuracy and measurement trueness answer different questions from precision. A common additive offset leaves the deviations $x_j-\bar{x}$, and hence $s$, unchanged. Averaging more independent readings can reduce random uncertainty in the mean but does not by itself remove that common offset.^[ref]

A useful physical study repeatedly removes and replaces the reference object while recording load procedure, environmental conditions and elapsed time. Specify which parts of the measurement were repeated: repeated display readings alone may omit placement variation or instrumental drift. The statistic describes the stated experiment, not an unconditional property of the instrument.