Spearman Rank Correlation

src.meliora.core.spearman_corr(array_1, array_2, alternative='two-sided')[source]

Calculate a Spearman correlation coefficient with associated p-value. This is a wrapper around scipy.stats.spearmanr function. The Spearman rank-order correlation coefficient is a nonparametric measure of the monotonicity of the relationship between two datasets. Unlike the Pearson correlation, the Spearman correlation does not assume that both datasets are normally distributed. Like other correlation coefficients, this one varies between -1 and +1 with 0 implying no correlation. Correlations of -1 or +1 imply an exact monotonic 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 Spearman 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

  • array_1 (pandas series) – Series containing multiple observations

  • array_2 (pandas series) – Series containing multiple observations

  • alternative ({'two-sided', 'less', 'greater'}, optional) – Defines the alternative hypothesis. Default is ‘two-sided’. The following options are available: * ‘two-sided’: the correlation is nonzero * ‘less’: the correlation is negative (less than zero) * ‘greater’: the correlation is positive (greater than zero)

Returns

  • correlation (float or ndarray (2-D square)) – Spearman correlation matrix or correlation coefficient (if only 2 variables are given as parameters. Correlation matrix is square with length equal to total number of variables (columns or rows) in a and b combined.

  • pvalue (float) – The p-value for a hypothesis test whose null hypotheisis is that two sets of data are uncorrelated. See alternative above for alternative hypotheses. pvalue has the same shape as correlation.

References

[1] Zwillinger, D. and Kokoska, S. (2000). CRC Standard Probability and Statistics Tables and Formulae. Chapman & Hall: New York. 2000. Section 14.7

Examples

>>> spearmanr([1,2,3,4,5], [5,6,7,8,7])
SpearmanrResult(correlation=0.82078..., pvalue=0.08858...)