Chauvenet's criterion

In statistical theory, the Chauvenet's criterion (named for William Chauvenet^[1]) is a means of assessing whether one piece of experimental data — an outlier — from a set of observations, is likely to be spurious.

To apply Chauvenet's criterion, first calculate the mean and standard deviation of the observed data. Based on how much the suspect datum differs from the mean, use the normal distribution function (or a table thereof) to determine the probability that a given data point will be at the value of the suspect data point. Multiply this probability by the number of data points taken. If the result is less than 0.5, the suspicious data point may be discarded, i.e., a reading may be rejected if the probability of obtaining the particular deviation from the mean is less than 1/(2n).

Example

For instance, suppose a value is measured experimentally in several trials as 9, 10, 10, 10, 11, and 50. The mean is 16.7 and the standard deviation 16.34. 50 differs from 16.7 by 33.3, slightly more than two standard deviations. The probability of taking data more than two standard deviations from the mean is roughly 0.05. Six measurements were taken, so the statistic value (data size multiplied by the probability) is 0.05×6 = 0.3. Because 0.3 < 0.5, according to Chauvenet's criterion, the measured value of 50 should be discarded (leaving a new mean of 10, with standard deviation 0.7).

Peirce's criterion

Another method for eliminating spurious data is called Peirce's criterion. It was developed a few years before Chauvenet's criterion was published, and it is a more rigorous approach to the rational deletion of outlier data. See S. Ross reference below. Other methods such as Grubbs' test for outliers are mentioned under the listing for Outlier.

Criticism

Deletion of outlier data is a controversial practice frowned on by many scientists and science instructors; while Chauvenet's criterion provides an objective and quantitative method for data rejection, it does not make the practice more scientifically or methodologically sound, especially in small sets or where a normal distribution cannot be assumed. Rejection of outliers is more acceptable in areas of practice where the underlying model of the process being measured and the usual distribution of measurement error are confidently known.

References

1. ^ Chauvenet, William. A Manual of Spherical and Practical Astronomy V. II. 1863. Reprint of 1891. 5th ed. Dover, N.Y.: 1960. pp. 474 - 566.

• Taylor, John R. An Introduction to Error Analysis. 2nd edition. Sausalito, California: University Science Books, 1997. pp 166-8.

• Stephen Ross, PhD, University of New Haven article, J. Engr. Technology, Fall, 2003. [1]

• Barnett, Vic and Lewis, Toby. "Outliers in Statistical Data". 3rd edition. Chichester: J.Wiley and Sons, 1994. ISBN: 0 471 930 94 6.

• Aicha Zerbet, Mikhail Nikulin. A new statistics for detecting outliers in exponential case, Communications in Statistics: Theory and Methods, 2003, v.32, pp.573-584.