# scipy.stats.pointbiserialr¶

scipy.stats.pointbiserialr(x, y)[source]

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

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 uses a shortcut formula but produces the same result as pearsonr.

Parameters: x : array_like of bools Input array. y : array_like Input array. correlation : float R value pvalue : float 2-tailed p-value
rac{overline{Y_{1}} -
overline{Y_{0}}}{s_{y}}sqrt{

rac{N_{1} N_{2}}{N (N - 1))}}

Where $$Y_{0}$$ and $$Y_{1}$$ 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 $$r_{pb}$$ 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 $$r_{pb}$$ is nonzero. The relation between the t-statistic for comparing two independent groups and $$r_{pb}$$ is given by:

$t = \sqrt{N - 2}$

rac{r_{pb}}{sqrt{1 - r^{2}_{pb}}}

Examples

>>> from scipy import stats
>>> a = np.array([0, 0, 0, 1, 1, 1, 1])
>>> b = np.arange(7)
>>> stats.pointbiserialr(a, b)
(0.8660254037844386, 0.011724811003954652)
>>> stats.pearsonr(a, b)
(0.86602540378443871, 0.011724811003954626)
>>> np.corrcoef(a, b)
array([[ 1.       ,  0.8660254],
[ 0.8660254,  1.       ]])


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