`scipy.stats._stats_py:pointbiserialr`

source: /scipy/stats/_stats_py.py :5431

Signature

   def     pointbiserialr (    x    ,    y    ,  * ,     axis    =  0   ,    nan_policy    =  propagate   ,    keepdims    =  False     )

Summary

Calculate a point biserial correlation coefficient and its p-value.

Extended Summary

The point biserial correlation is used to measure the relationship between a binary variable, x, and a continuous variable, y. Like other correlation coefficients, this one varies between -1 and +1 with 0 implying no correlation. Correlations of -1 or +1 imply a determinative relationship.

This function may be computed using a shortcut formula but produces the same result as pearsonr.

Parameters

x : array_like of bools

Input array.

y : array_like

Input array.

axis : int or None, default: 0

If an int, the axis of the input along which to compute the statistic. The statistic of each axis-slice (e.g. row) of the input will appear in a corresponding element of the output. If None, the input will be raveled before computing the statistic.

nan_policy : {'propagate', 'omit', 'raise'}

Defines how to handle input NaNs.

propagate: if a NaN is present in the axis slice (e.g. row) along which the statistic is computed, the corresponding entry of the output will be NaN.
omit: NaNs will be omitted when performing the calculation. If insufficient data remains in the axis slice along which the statistic is computed, the corresponding entry of the output will be NaN.
raise: if a NaN is present, a ValueError will be raised.

keepdims : bool, default: False

If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the input array.

Returns

: res: SignificanceResult

An object containing attributes:

statistic: statistic
pvalue: pvalue

Notes

pointbiserialr uses a t-test with n-1 degrees of freedom. It is equivalent to pearsonr.

The value of the point-biserial correlation can be calculated from:

r_{p b} = \frac{Y _{1} - Y _{0}}{s _{y}} \frac{N _{0} N _{1}}{N ( N - 1 )}

Where $\overline{Y_{0}}$ and $\overline{Y_{1}}$ are means of the metric observations coded 0 and 1 respectively; $N_{0}$ and $N_{1}$ are number of observations coded 0 and 1 respectively; $N$ is the total number of observations and $s_{y}$ is the standard deviation of all the metric observations.

A value of $r_{p b}$ that is significantly different from zero is completely equivalent to a significant difference in means between the two groups. Thus, an independent groups t Test with $N - 2$ degrees of freedom may be used to test whether $r_{p b}$ is nonzero. The relation between the t-statistic for comparing two independent groups and $r_{p b}$ is given by:

t = N - 2 \frac{r _{p b}}{1 - r _{p b}^{2}}

Beginning in SciPy 1.9, np.matrix inputs (not recommended for new code) are converted to np.ndarray before the calculation is performed. In this case, the output will be a scalar or np.ndarray of appropriate shape rather than a 2D np.matrix. Similarly, while masked elements of masked arrays are ignored, the output will be a scalar or np.ndarray rather than a masked array with mask=False.

Array API Standard Support

pointbiserialr has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ⛔                   
PyTorch               ⛔                     ⛔                   
JAX                   ⛔                     ⛔                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

import numpy as np
from scipy import stats
a = np.array([0, 0, 0, 1, 1, 1, 1])
b = np.arange(7)

✓

stats.pointbiserialr(a, b)
stats.pearsonr(a, b)
np.corrcoef(a, b)