Pearsonr

pearsonr

Metric pearsonr from scipy.stats (scipy.stats.pearsonr)

When to invoke this skill

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

Reference signature

from scipy.stats import pearsonr

# pearsonr(x, y, *, alternative='two-sided', method=None, axis=0)

Library docstring

Pearson correlation coefficient and p-value for testing non-correlation.

The Pearson correlation coefficient [1]_ measures the linear relationship
between two datasets. Like other correlation
coefficients, this one varies between -1 and +1 with 0 implying no
correlation. Correlations of -1 or +1 imply an exact linear relationship.
Positive correlations imply that as x increases, so does y. Negative
correlations imply that as x increases, y decreases.

This function also performs a test of the null hypothesis that the
distributions underlying the samples are uncorrelated and normally
distributed. (See Kowalski [3]_
for a discussion of the effects of non-normality of the input on the
distribution of the correlation coefficient.)
The p-value roughly indicates the probability of an uncorrelated system
producing datasets that have a Pearson correlation at least as extreme
as the one computed from these datasets.

Parameters
----------
x : array_like
    Input array.
y : array_like
    Input array.
axis : int or None, default
    Axis along which to perform the calculation. Default is 0.
    If None, ravel both arrays before performing the calculation.

    .. versionadded:: 1.14.0
alternative : {'two-sided', 'greater', 'less'}, optional
    Defines the alternative hypothesis. Default is 'two-sided'.
    The following options are available:

    * 'two-sided': the correlation is nonzero
    * 'less': the correlation is negative (less than zero)
    * 'greater':  the correlation is positive (greater than zero)

    .. versionadded:: 1.9.0
method : ResamplingMethod, optional
    Defines the method used to compute the p-value. If `method` is an
    instance of `PermutationMethod`/`MonteCarloMethod`, the p-value is
    computed using
    `scipy.stats.permutation_test`/`scipy.stats.monte_carlo_test` with the
    provided configuration options and other appropriate settings.
    Otherwise, the p-value is computed as documented in the notes.

    .. versionadded:: 1.11.0

Returns
-------
result : `~scipy.stats._result_classes.PearsonRResult`
    An object with the following attributes:

    statistic : float
        Pearson product-moment correlation coefficient.
    pvalue

Quick recipe

import scipy.stats as _m
score = _m.pearsonr(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).