Cochran's C test

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Cochran's C-Test is a statistical test that can be used to check whether a single variance is significantly greater than a set of existing variances. The test was presented by William G. Cochran in 1941 and should not be confused with Cochran's Q-Test .

The C-test is used in particular to check the quality of measurements by laboratories. It is recommended in ISO 5725 ("Accuracy (trueness and precision) of measurement methods and results") to check the hypothesis that "there are only minor differences in the variances within the laboratory between the laboratories".

Test scenario

The C-test provides a criterion for deciding whether a set of variances is present

  • a) is homogeneous or whether
  • b) the highest value is significantly different from the others.

The decision is interpreted inductively statistically in such a way that it is calculated how probable it is that all samples whose variances exist were drawn from the same population despite their differences with regard to the known parameter variance.

Action

The test statistic C is calculated as follows:

where:

C j = Cochran's C for data series j
S j = standard deviation of data series j
N = number of data series
S i = standard deviation of data series i (1 ≤ i ≤ N )

Where j is the data series with the greatest variance. The test value calculated in this way is then compared with the critical values tabulated by Cochran , the value in the table depending on the number of compared values ​​and the number of degrees of freedom of the variance. The number of degrees of freedom df of the variance is for a data series of length n df = n-1 .

requirements

The following requirements apply to the Cochran's C-Test:

  • All data series must have the same scope ( balanced design ).
  • The measured values ​​within each data series must be normally distributed.

If the data series to be compared are of different sizes, it is possible to use the critical value for the smallest data series size. The test is then correspondingly more conservative.

literature

  • WG Cochran (1941): The distribution of the largest of a set of estimated variances as a fraction of their total. In: Annuals of Human Genetics , Vol. 11, Issue 1, January 1941, pp. 47-52, doi : 10.1111 / j.1469-1809.1941.tb02271.x .
  • International Organization for Standardization (1994). ISO 5725-2: 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, Geneva.

Web links

Individual evidence

  1. ↑ 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 ; Section 7.3.3.1
  2. ↑ https://consultglp.com/wp-content/uploads/2015/07/cochran-c-test-for-outliers.pdf
  3. ↑ Gerald van Belle, Lloyd D. Fisher, Patrick J. Heagerty and Thomas Lumley: Biostatistics. A Methodology for the Health Sciences . 2nd Edition. Hoboken, NY 2004, ISBN 0-471-03185-2 , pp. 402 .