scipy.stats.pearsonr

scipy.stats.pearsonr(x, y)

Calculate a Pearson correlation coefficient and the p-value for testing non-correlation.

The Pearson correlation coefficient measures the linear relationship between two datasets. Strictly speaking, Pearson’s correlation requires that each dataset be normally distributed, and not necessarily zero-mean. 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.

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. The p-values are not entirely reliable but are probably reasonable for datasets larger than 500 or so.

Parameters:

x : (N,) array_like

Input

y : (N,) array_like

Input

Returns:

r : float

Pearson’s correlation coefficient

p-value : float

2-tailed p-value

Notes

The correlation coefficient is calculated as follows:

\[r_{pb} = \frac{\sum (x - m_x) (y - m_y)} {\sqrt{\sum (x - m_x)^2 \sum (y - m_y)^2}}\]

where \(m_x\) is the mean of the vector \(x\) and \(m_y\) is the mean of the vector \(y\).

References

http://www.statsoft.com/textbook/glosp.html#Pearson%20Correlation

Examples

>>> from scipy import stats
>>> a = np.array([0, 0, 0, 1, 1, 1, 1])
>>> b = np.arange(7)
>>> stats.pearsonr(a, b)
(0.8660254037844386, 0.011724811003954654)

>>> stats.pearsonr([1,2,3,4,5], [5,6,7,8,7])
(0.83205029433784372, 0.080509573298498519)