Fast computation of the exact null distribution of Spearman's rho and Page's L statistics for samples with and without ties

Abstract We present a new algorithm for computing the exact null distribution of the Spearman rank correlation statistic ρ , which also works in the case of ties. The algorithm is based on symmetries in the representation of the probability generating function as a permanent with monomial entries. We present new critical values for sample sizes 19⩽ n ⩽22. Finally, we show how to derive the exact null distribution of Page's L statistic from the null distribution of ρ .

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