Accuracy and Precision

Level 0 (green)- this is basic material that you have probably encountered already, although the approach may be slightly different. No prior knowledge is assumed.

Experimental errors are of two basic types:randomandsystematic.

Random errors

Random errors are not repeatable and lead to fluctuations in results.

Repetitions of the same experiment lead to different results.

Random errors can arise from
the finite precision of the measuring apparatus, e.g. the least step
fluctuations in the environment -for example temperature
truly random phenomena -for example radioactive decay.

Systematic errors

A systematic error is repeatable and means that the experimental measurements are centred on the wrong target.

Systematic errors can arise from
operator error - for example blowing out the last drop from a pipette
impurities in the sample
calibration of the instrument or the standard
incorrect theory

Accuracy and precision

Precision measures random errors, i.e. how closely measurements are grouped. The precision of a measurement says nothing about whether the measurements are grouped about the correct value.

It is possible to estimate precision by analysing repetitions of an experiment. The aim of statistics is to find optimal ways of extracting data and estimating errors from such sets of measurements.

Accuracy measures how close measurements are to the "correct" value, and is a stronger statement than precision, as it includes both random and systematic errors. To assess accuracy the true result must already be known.

If all sources of systematic error are removed, it may be reasonable to claim that a result is accurate, but this might change if another course of systematic error is found.

Comparison of measurements of the same quantity by different methods may sometimes reveal systematic differences, if the measurements are sufficiently precise. Measurements of the density of "nitrogen" generalted chemically and "nitrogen" prepared from air famously led to the discovery of the noble gases (see problems.)