What is "probable error"

Probable \Prob"a*ble\, a. [L. probabilis, fr. probare to try, approve, prove: cf. F. probable. See Prove, and cf. Provable.]

1. Capable of being proved. [Obs.]

2. Having more evidence for than against; supported by evidence which inclines the mind to believe, but leaves some room for doubt; likely.

   That is accounted probable which has better arguments producible for it than can be brought against it.
   --South.

   I do not say that the principles of religion are merely probable; I have before asserted them to be morally certain.
   --Bp. Wilkins.

3. Rendering probable; supporting, or giving ground for, belief, but not demonstrating; as, probable evidence; probable presumption.
   --Blackstone.

   Probable cause (Law), a reasonable ground of presumption that a charge is, or my be, well founded.

   Probable error (of an observation, or of the mean of a number), that within which, taken positively and negatively, there is an even chance that the real error shall lie. Thus, if 3[sec] is the probable error in a given case, the chances that the real error is greater than 3[sec] are equal to the chances that it is less. The probable error is computed from the observations made, and is used to express their degree of accuracy.

   The probable, that which is within the bounds of probability; that which is not unnatural or preternatural; -- opposed to the marvelous.

Error \Er"ror\, n. [OF. error, errur, F. erreur, L. error, fr. errare to err. See Err.]

1. A wandering; a roving or irregular course. [Obs.]

   The rest of his journey, his error by sea.
   --B. Jonson.

2. A wandering or deviation from the right course or standard; irregularity; mistake; inaccuracy; something made wrong or left wrong; as, an error in writing or in printing; a clerical error.

3. A departing or deviation from the truth; falsity; false notion; wrong opinion; mistake; misapprehension.

   His judgment was often in error, though his candor remained unimpaired.
   --Bancroft.

4. A moral offense; violation of duty; a sin or transgression; iniquity; fault.
   --Ps. xix. 12.

5. (Math.) The difference between the approximate result and the true result; -- used particularly in the rule of double position.

6. (Mensuration)

   1. The difference between an observed value and the true value of a quantity.

   2. The difference between the observed value of a quantity and that which is taken or computed to be the true value; -- sometimes called residual error.

7. (Law.) A mistake in the proceedings of a court of record in matters of law or of fact.

8. (Baseball) A fault of a player of the side in the field which results in failure to put out a player on the other side, or gives him an unearned base.

   Law of error, or Law of frequency of error (Mensuration), the law which expresses the relation between the magnitude of an error and the frequency with which that error will be committed in making a large number of careful measurements of a quantity.

   Probable error. (Mensuration) See under Probable.

   Writ of error (Law), an original writ, which lies after judgment in an action at law, in a court of record, to correct some alleged error in the proceedings, or in the judgment of the court.
   --Bouvier. Burrill.

   Syn: Mistake; fault; blunder; failure; fallacy; delusion; hallucination; sin. See Blunder.

In statistics, probable error defines the half-range of an interval about a central point for the distribution, such that half of the values from the distribution will lie within the interval and half outside. Thus it is equivalent to half the interquartile range, or the median absolute deviation. The probable error can also be expressed as a multiple of the standard deviation σ, γ = 0.6745 × σ (where the multiplying factor 0.6745 derives from the normal distribution), which requires that at least the second statistical moment of the distribution should exist, whereas the other definition does not. One use of the term probable error in statistics is as the name for the scale parameter of the Cauchy distribution.