SciPy

scipy.stats.mstats.pointbiserialr

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

Calculates a point biserial correlation coefficient and the associated 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.

Returns :

r : float

R value

p-value : float

2-tailed p-value

Notes

Missing values are considered pair-wise: if a value is missing in x, the corresponding value in y is masked.

References

http://en.wikipedia.org/wiki/Point-biserial_correlation_coefficient

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.       ]])