# Peirce's criterion

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Peirce's criterion

Peirce's criterion is a method, devised by Benjamin Peirce, that may be used to eliminate suspect experimental data using probability theory.

Description

For scientists, engineers and others involved in real data collection, the situation often arises in which one or more of the measured values appears to be outside the usual range. The temptation to ignore this data with rationalisations such as blaming faulty recording equipment ( the equipment had a power surge, there was dirt in the lens) should be resisted. Instead of arbitrarily dropping data, Peirce's Criterion (1) may be applied. The possibility of more than one suspect experimental data value is also included.

The method is similar to the commonly used "Chauvenet's criterion"; however, Peirce's criterion is a more rigorous theoretical development based on the Gaussian distribution which can be applied to more than one suspect data value. In fact, Chauvenet refers to the prior work of Peirce, writing, in his original work: "What I have given may serve the purpose of giving the reader greater confidence in the correctness and value of Peirce's criterion."

The method can be applied using a table which lists criterion values corresponding to the number of data values. The table in reference 2 allows for up to 60 data measurements. Hawkins (3) provides a formula for the criterion.

ee also

*Outlier

References

1.Benjamin Peirce, [http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1852AJ......2..161P;data_type=PDF_HIGH "Criterion for the Rejection of Doubtful Observations"] , Astronomical Journal II 45 (1852) and [http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1852AJ......2..176P;data_type=PDF_HIGH "Errata to the original paper"] .

2. Stephen Ross, "Peirce's Criterion for the Elimination of Suspect Experimental Data", J. Engr. Technology, Fall, 2003. [http://newton.newhaven.edu/sross/piercescriterion.pdf]

3. D.M. Hawkins (1980). Identification of outliers. Chapman and Hall, London. p10

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