Wilcoxon

---
name: wilcoxon
description: Compute the wilcoxon metric — provided by scipy.stats. Use when the user has predictions and ground-truth and needs to compute wilcoxon, or asks how to score with wilcoxon.
metadata:
  skill_kind: metric
  source_lib: scipy.stats
  import_path: scipy.stats.wilcoxon
  source: library_introspection
---

# wilcoxon

> Metric `wilcoxon` from `scipy.stats` (scipy.stats.wilcoxon)

## When to invoke this skill

The user has predictions + ground truth and asks to evaluate with wilcoxon, or
mentions `scipy.stats.wilcoxon` directly, or wants the standard scipy.stats implementation.

## Reference signature

```python
from scipy.stats import wilcoxon

# wilcoxon(x, y=None, zero_method='wilcox', correction=False, alternative='two-sided', method='auto', *, axis=0, nan_policy='propagate', keepdims=False)
```

## Library docstring

```
Calculate the Wilcoxon signed-rank test.

The Wilcoxon signed-rank test tests the null hypothesis that two
related paired samples come from the same distribution. In particular,
it tests whether the distribution of the differences ``x - y`` is symmetric
about zero. It is a non-parametric version of the paired T-test.

Parameters
----------
x : array_like
    Either the first set of measurements (in which case ``y`` is the second
    set of measurements), or the differences between two sets of
    measurements (in which case ``y`` is not to be specified.)  Must be
    one-dimensional.
y : array_like, optional
    Either the second set of measurements (if ``x`` is the first set of
    measurements), or not specified (if ``x`` is the differences between
    two sets of measurements.)  Must be one-dimensional.

    .. warning::
        When `y` is provided, `wilcoxon` calculates the test statistic
        based on the ranks of the absolute values of ``d = x - y``.
        Roundoff error in the subtraction can result in elements of ``d``
        being assigned different ranks even when they would be tied with
        exact arithmetic. Rather than passing `x` and `y` separately,
        consider computing the difference ``x - y``, rounding as needed to
        ensure that only truly unique elements are numerically distinct,
        and passing the result as `x`, leaving `y` at the default (None).
zero_method : {"wilcox", "pratt", "zsplit"}, optional
    There are different conventions for handling pairs of observations
    with equal values ("zero-differences", or "zeros").

    * "wilcox": Discards all zero-differences (default); see [4]_.
    * "pratt": Includes zero-differences in the ranking process,
      but drops the ranks of the zeros (more conservative); see [3]_.
      In this case, the normal approximation is adjusted as in [5]_.
    * "zsplit": Includes zero-differences in the ranking process and
      splits the zero rank between positive and negative ones.
correction : bool, optional
    If True, apply continuity correction by adjusting the Wilcoxon rank
    statistic by 0.5 towards the mean value when computing the
    z-statistic if a normal approximat
```

## Quick recipe

```python
import scipy.stats as _m
score = _m.wilcoxon(y_true, y_pred)
```

## Don'ts

- Don't reimplement when the library version handles edge cases (NaN, ties, empty inputs) better than a hand-rolled formula.
- Always check the library version's argument order — sklearn is `(y_true, y_pred)` while torchmetrics is `(preds, target)`.