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We consider M ≥ 2 independent polynomial samples with N outcomes. For the case when M and N are fixed but sizes of samples tend to infinity we find limit distributions of a new statistic σ 2 : chi-square distribution with (M−1)(N−1) degrees of freedom if samples are statistically homogeneous, non-central chisquare distribution with the same number of degrees of freedom if samples are «convergent» to homogeneous ones, and normal distribution if samples are statistically nonhomogeneous.

On a statistic for testing the homogeneity of polynomial samples