What's the meaning of negative accuracy for measurements of physical quantities? Can measured values of a physical quantity ever have a negative accuracy?

I read some materials about accuracy and am still confused.

The Wikipedia article http://en.wikipedia.org/wiki/Accuracy_and_precision explains the accuracy as defined for interpreting observed values of a random variable which has certain probability distribution. I am not sure how much the interpretation is applicable to measurement of physical quantities as probability isn't necessarily a well-defined physical quantity.

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    $\begingroup$ Depends on you exact definition of accuracy. Sometimes this $| x_\text{observed} - x_\text{actual}|$, and sometimes it is a logarithm of that. $\endgroup$ – Sasha Nov 28 '11 at 21:03
  • $\begingroup$ As with Sasha the meanings of "accuracy" I'm familiar with are generally non-negative. Do you mean the "residual" or the "fractional residual"? $\endgroup$ – dmckee --- ex-moderator kitten Nov 29 '11 at 1:45
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    $\begingroup$ The only place where "negative" is found in the link you provide is in "binary classification", yes/no tests, and even there accuracy as defined is only a positive number. You must be misunderstanding something. $\endgroup$ – anna v Nov 29 '11 at 4:58
  • $\begingroup$ Maybe You are not familiar with the math. symbol for absolut value? $\endgroup$ – Georg Nov 30 '11 at 9:42
  • $\begingroup$ Can accuracy as defined as reference.wolfram.com/mathematica/ref/Accuracy.html has a nontrivial use/meaning when it's negative? It says "... With uncertainty dx, Accuracy[x] is -Log[10, dx] ..." $\endgroup$ – Computist Nov 30 '11 at 21:17

The accuracy is either a measure of the width of a Gaussian model of error, or it is a confidence interval width. It is always positive, never negative, and there are no circumstances in which a negative accuracy makes sense.

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    $\begingroup$ Though I would add that the plot in the wiki link is misleading. What the plot calls accuracy is the systematic error, and systematic errors can be positive or negative. We call a measurement accurate when the gausian of the measurements is centered on the true value. The distinction between the concept of accuracy and the concept of precision is necessary as long as there are systematic errors in the measurements. $\endgroup$ – anna v Jan 29 '12 at 8:03

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