In the commentary of a statistical analysis, one often reads, hears or makes references to the properties of "error bars", which are a convenient way of plotting the mismatch between a dataset and a model of some sort. Yet the mismatch between a dataset and a model or two datasets may be the result of processes that can have very different consequences on the data's further interpretation.
A mismatch can be due to some level of uncertainty on the measurement: things like temporal fluctuations imposed by observing conditions (seeing, general atmospheric condition) or by the probabilistic nature of the phenomenon at work (photon detection) or limitations in the resolution of the measurement. If you perform repeated measurements, you will observe a scatter in the value. The variance associated to the measurement will decrease with the number of measurements and generally roughly follow a 1/sqrt(N) law.
A mismatch can also be due to a systematic or calibration error in the measuring chain: a static temperature offset between consecutive series of measurements, a change in the aberrations of the telescope, two targets with different spectral types. The variance associated to the measurement may follow the 1/sqrt(N) law, but the bias will remain: even if your precision is good, your measurement may lack accuracy.
The following "game" illustrates the difference between
these two notions of precision and
accuracy. So play the game: just aim for the center of
the target and empty your charger. After each run, the
statistical properties of your shooting is provided. Watch for
the impact of both accuracy and precision on the mean and
standard deviation of the final result!
| Not accurate | Accurate | |
Not-precise |
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Precise |
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