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ZeroMethod

How the Wilcoxon signed-rank test treats pairs whose difference is zero.

public enum ZeroMethod { Wilcox, Pratt, ZSplit }

Members — Wilcox discards the zero-difference pairs before ranking; scipy's 'wilcox', and the default. Pratt ranks the zeros alongside everything else, then drops their ranks from the sums; scipy's 'pratt'. ZSplit ranks the zeros the same way and splits their rank sum evenly between the two sums; scipy's 'zsplit'.

Example — the same seven pairs, two of them unchanged, read three different ways.

using Lodestar.Stats;

double[] before = [12.0, 9.0, 15.0, 11.0, 8.0, 14.0, 10.0, 13.0];
double[] after = [9.0, 6.0, 16.0, 11.0, 4.0, 15.0, 10.0, 17.0];

TestResult wilcox = Wilcoxon.Paired(before, after, ZeroMethod.Wilcox);
TestResult pratt = Wilcoxon.Paired(before, after, ZeroMethod.Pratt);
TestResult zsplit = Wilcoxon.Paired(before, after, ZeroMethod.ZSplit);

double wilcoxW = wilcox.Statistic;   // => 8.5
double prattW = pratt.Statistic;     // => 14.5
double zsplitW = zsplit.Statistic;   // => 16

Remarks — three rules, three different statistics on the same data. This is why zeroMethod is part of the test's definition rather than a tuning knob: Wilcox ranks only the five non-zero differences, so its statistic sits on a different scale entirely from Pratt's and ZSplit's, which both rank all eight values and only differ in what happens to the zero group's ranks afterwards — dropped for Pratt, split for ZSplit.

Pratt and ZSplit can share a p-value even when their statistics differ. Under the permutation route both zero methods here land on — the sample is small and carries zeros, so ExactMethod.Auto falls to the exhaustive test rather than the plain exact table — the p-value is computed from the raw positive and negative rank sums, before ZSplit's even split is added; Pratt and ZSplit compute that raw sum identically; only Wilcox's p-value, built from a genuinely smaller ranked set, is free to land somewhere else. Measured here: all three give 0.7188, 0.8438, 0.8438 — Wilcox reads differently, Pratt and ZSplit agree past three digits on this route even though their statistics, 14.5 and 16, do not.

Applies to — net10.0, netstandard2.0.

See also — Wilcoxon.Paired, Wilcoxon.OneSample, the Python equivalence table.