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given the observed ranks, using an implementation of the
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given the observed ranks, using an implementation of the
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\I{Streitberg}--\I{Röhmel} shift algorithm
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\I{Streitberg}--\I{Röhmel} shift algorithm
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\bibcitep{R:Streitberg+Roehmel:1986, R:Streitberg+Roehmel:1987}
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\bibcitep{R:Streitberg+Roehmel:1986, R:Streitberg+Roehmel:1987}
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contributed by \I{Torsten Hothorn}.
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contributed by \I{Torsten Hothorn}.
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If the normal approximation is used and there are no ties, improved
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If the normal approximation is used, improved
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asymptotic p-values can be obtained via including up to \eqn{k = 3}
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asymptotic p-values can be obtained via including up to \eqn{k = 3}
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correction terms of the \I{Edgeworth} series for the normal approximation,
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correction terms of the \I{Edgeworth} series for the normal
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approximation.
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For the signed rank test, this employs the formulas given in
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as given in \bibcitet{R:Fellingham+Stoker:1964} for the signed rank
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\bibcitet{R:Fellingham+Stoker:1964} if there are no ties or zeros.
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For the rank sum test, this is only available if there are no ties,
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test and in \bibcitet{R:Fix+Hodges_Jr_:1955} for the rank sum test.
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and uses \bibcitet{R:Fix+Hodges_Jr_:1955}.
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For stability reasons, it may be advisable to use rounded data or to set
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For stability reasons, it may be advisable to use rounded data or to set
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\code{digits.rank = 7}, say, such that determination of ties does not
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\code{digits.rank = 7}, say, such that determination of ties does not
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depend on very small numeric differences (see the example).
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depend on very small numeric differences (see the example).
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