Differential analysis & tests / Wilcoxon signed-rank test
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The Wilcoxon signed-rank test is the non-parametric counterpart of the paired t-test: it ranks the within-subject differences and tests whether their distribution is centred on 0, without assuming normality.
Difference = first group − second group. V (= R⁺) is the rank sum of positive differences; the matched-pairs rank-biserial correlation = (R⁺ − R⁻)/(R⁺ + R⁻), between −1 and 1.
Zero differences are discarded by default (Wilcoxon); Pratt’s method ranks them before discarding, and zsplit splits their ranks between the positive and negative sums.
P values: exact distribution without ties or zeros for n ≤ 50; exact enumeration of all sign flips with ties or zeros for n ≤ 13; otherwise the normal approximation. The Hodges–Lehmann pseudo-median is the median of all Walsh averages.
Wilcoxon F. (1945) Biometrics Bulletin 1:80–83; Pratt J. W. (1959) J Am Stat Assoc 54:655–667. Statistic and P match scipy.stats.wilcoxon; the pseudo-median CI follows Tukey’s method (normal approximation, no tie correction).
Up to 100,000 rows.
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