Compute correlation coefficients with uncertainties

# pymccorrelation

A tool to calculate correlation coefficients for data, using bootstrapping and/or perturbation to estimate the uncertainties on the correlation coefficient. This was initially a python implementation of the Curran (2014) method for calculating uncertainties on Spearman's Rank Correlation Coefficient, but has since been expanded. Curran's original C implementation is MCSpearman (ASCL entry).

Currently the following correlation coefficients can be calculated (with bootstrapping and/or perturbation):

Kendall's tau can also calculated when some of the data are left/right censored, following the method described by Isobe+1986.

• python3
• scipy
• numpy

## Installation

pymccorrelation is available via PyPi and can be installed with:

pip install pymccorrelation


## Usage

pymccorrelation exports a single function to the user (also called pymccorrelation).

from pymccorrelation import pymccorrelation



The correlation coefficient can be one of pearsonr, spearmanr, or kendallt.

For example, to compute the Pearson's r for a sample, using 1000 bootstrapping iterations to estimate the uncertainties:

res = pymccorrelation(data['x'], data['y'],
coeff='pearsonr',
Nboot=1000)


The output, res is a tuple of length 2, and the two elements are:

• numpy array with the correlation coefficient (Pearson's r, in this case) percentiles (by default 16%, 50%, and 84%)
• numpy array with the p-value percentiles (by default 16%, 50%, and 84%)

The percentile ranges can be adjusted using the percentiles keyword argument.

Additionally, if the full posterior distribution is desired, that can be obtained by setting the return_dist keyword argument to True. In that case, res becomes a tuple of length four:

• numpy array with the correlation coefficient (Pearson's r, in this case) percentiles (by default 16%, 50%, and 84%)
• numpy array with the p-value percentiles (by default 16%, 50%, and 84%)
• numpy array with full set of correlation coefficient values from the bootstrapping
• numpy array with the full set of p-values computed from the bootstrapping

Please see the docstring for the full set of arguments and information including measurement uncertainties (necessary for point perturbation) and for marking censored data.

## Citing

If you use this script as part of your research, I encourage you to cite the following papers:

• Curran 2014: Describes the technique and application to Spearman's rank correlation coefficient
• Privon+ 2020: First use of this software, as pymcspearman.

Please also cite scipy and numpy.

If your work uses Kendall's tau with censored data please also cite:

• Isobe+ 1986: Censoring of data when computing Kendall's rank correlation coefficient.

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