# Cochran´s Q Statistic

Cochran´s Q Statistic:

Cochran´s Q statistic is computed from replicated measurements data with binary responses. This statistic tests a difference in effects among 2 or more treatments applied to the same set of experimental units.

Consider the results of a study of M treatments applied to N experimental units (e.g patients or laboratory animals). The outcomes of individual measurements for the (i)th treatment of the (j)th unit are binary variables {Vij;   i=1,…,M;   j=1,…,N} taking on two values “0” or “1” (e.g. “No effect” or “Effect is found”).

The Cochran Q statistic is computed by the formula

Q =
 M(M–1) M ÃƒÂ¥ i=1 (Gi – mean(G)   )2

 M N ? j=1 Lj – N

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