Cochran's C test

Cochran's test,[1] named after William G. Cochran, is a one-sided upper limit variance outlier statistical test . The C test is used to decide if a single estimate of a variance (or a standard deviation) is significantly larger than a group of variances (or standard deviations) with which the single estimate is supposed to be comparable. The C test is discussed in many text books [2][3][4] and has been recommended by IUPAC[5] and ISO.[6] Cochran's C test should not be confused with Cochran's Q test, which applies to the analysis of two-way randomized block designs.

The C test assumes a balanced design, i.e. the considered full data set should consist of individual data series that all have equal size. The C test further assumes that each individual data series is normally distributed. Although primarily an outlier test, the C test is also in use as a simple alternative for regular homoscedasticity tests such as Bartlett's test, Levene's test and the Brown–Forsythe test to check a statistical data set for homogeneity of variances. An even simpler way to check homoscedasticity is provided by Hartley's Fmax test,[3] but Hartley's Fmax test has the disadvantage that it only accounts for the minimum and the maximum of the variance range, while the C test accounts for all variances within the range.

  1. ^ W.G. Cochran, The distribution of the largest of a set of estimated variances as a fraction of their total, Annals of Human Genetics (London) 11(1), 47–52 (January 1941).
  2. ^ D.L. Massart, B.G.M. Vandeginste, L.M.C. Buydens, S. de Jong, P.J. Lewi, J. Smeyers-Verbeke, Handbook of Chemometrics and Qualimetrics: Part A, Elsevier, Amsterdam, the Netherlands, 1997 ISBN 0-444-89724-0.
  3. ^ a b P. Konieczka, J. Namieśnik, Quality Assurance and Quality Control in the Analytical Chemical Laboratory – A Practical Approach, CRC Press, Boca Raton, Florida, 2009; ISBN 978-1-4200-8270-8.
  4. ^ J.K. Taylor, Quality Assurance of Chemical Measurements, 4th printing, Lewis Publishers, Chelsea, Michigan, 1988; ISBN 0-87371-097-5.
  5. ^ W. Horwitz, Harmonized protocol for the design and interpretation of collaborative studies, Trends in Analytical Chemistry 7(4), 118–120 (April 1988).
  6. ^ ISO Standard 5725–2:1994, “Accuracy (trueness and precision) of measurement methods and results – Part 2: Basic method for the determination of repeatability and reproducibility of a standard measurement method”, International Organization for Standardization, Geneva, Switzerland, 1994; http://www.iso.org/iso/iso_catalogue/catalogue_tc/catalogue_detail.htm?csnumber=11834