Cochran's C test

The C test detects one exceptionally large variance value at a time. The corresponding data series is then omitted from the full data set. According to ISO standard 5725 the C test may be iterated until no further exceptionally large variance values are detected, but such practice may lead to excessive rejections if the underlying data series are not normally distributed. The C test evaluates the ratio: ::C_j = \frac{S_j^2}{\displaystyle \sum_{i=1}^N S_i^2} where: :Cj = Cochran's C statistic for data series j :Sj = standard deviation of data series j :N = number of data series that remain in the data set; N is decreased in steps of 1 upon each iteration of the C test :Si = standard deviation of data series i (1 ≤ i ≤ N) The C test tests the null hypothesis (H0) against the alternative hypothesis (Ha): :H0: All variances are equal. :Ha: At least one variance value is significantly larger than the other variance values. ==Critical values==

The sample variance of data series j is considered an outlier at significance level α if Cj exceeds the upper limit critical value CUL. CUL depends on the desired significance level α, the number of considered data series N, and the number of data points (n) per data series. Selections of values for CUL have been tabulated at significance levels α = 0.01, α = 0.025, or using computer software for this function. ==Generalization==

The C test can be generalized to include unbalanced designs, one-sided lower limit tests and two-sided tests at any significance level α, for any number of data series N, and for any number of individual data points nj in data series j. ==See also==