The purpose of this paper is to give an exact criterion for testing whether all treatments are equal by a randomized block desing under the follwing conditions: 1.- The error variance differ from treatment to treatment. 2.- The error are correlated within a block but are independent from block to block- In a randomized block experiment when we are confronted with the problem of heterogeneous error variance or correlated erros, the ratio of the mean square for the treatments to the mean square for the error (obtained by pooling the sum of squares for error) is not distributed as Snedecor's F.

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