scipy.stats.pearsonr¶
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scipy.stats.
pearsonr
(x, y)[source]¶ 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:
\[r_{pb} = \frac{\sum (x - m_x) (y - m_y) }{\sqrt{\sum (x - m_x)^2 (y - m_y)^2}}\]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)