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In statistics, Cochran's theorem, devised by William G. Cochran, [1] is a theorem used to justify results relating to the probability distributions of statistics that are used in the analysis of variance.
The resulting sample size formula, is often applied with a conservative estimate of p (e.g., 0.5): ... A MATLAB script implementing Cochran's sample size formula;
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 effective sample size, ... Relatedly, Cochran (1977) provides a formula for the proportional increase in variance due to deviation from optimum allocation ...
Cochran's test is a non-parametric statistical test to verify whether k treatments have identical effects in the analysis of two-way randomized block designs where the response variable is binary. [ 1 ] [ 2 ] [ 3 ] It is named after William Gemmell Cochran .
where R 1 = N 11 + N 12 + N 13, and C 1 = N 11 + N 21, etc. . The trend test statistic is = (), where the t i are weights, and the difference N 1i R 2 −N 2i R 1 can be seen as the difference between N 1i and N 2i after reweighting the rows to have the same total.
William Gemmell Cochran (1909–1980), British statistician working in the United States, the person Cochran's theorem, Cochran's C test, Cochran's Q test and Cochran’s sample size formula were named for; William Kennedy-Cochran-Patrick (1896-1933), Scottish flying ace
Correction factor versus sample size n.. When the random variable is normally distributed, a minor correction exists to eliminate the bias.To derive the correction, note that for normally distributed X, Cochran's theorem implies that () / has a chi square distribution with degrees of freedom and thus its square root, / has a chi distribution with degrees of freedom.