Summary
The classical χ2 test of goodness of fit depends on the partition chosen to calculate it. In this work the covariance structure of the family of all χ2 tests obtained by translation (modulo 1) of a uniform partition of the interval [0, 1) it is determined, under the hypothesis of uniform distribution on [0, 1). This is used to define and compute an index which measure the indeterminacy of the χ2 test due to the arbitrary choice of the partition to compute it.
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Viollaz, A.J. On the reliability of the chi-square test. Metrika 33, 135–142 (1986). https://doi.org/10.1007/BF01894740
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DOI: https://doi.org/10.1007/BF01894740