The classical X 2 test of goodness of fit depends on the partition chosen to calculate it.In this work the covariance structure of the family of all • tests obtained by translation (modulo 1) of a uniform partition of the interval [0, 1) it is determined, undei the hypothesis of uniform distribution on [0, 1). This is used to define and compute an index which measure the indeterminacy of the • test due to the arbitrary choice of the partition to compute it.
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