Monte Carlo error analyses of Spearman's rank test

TL;DR

This paper introduces Monte Carlo methods to accurately estimate the uncertainties and probability distribution of Spearman's rank correlation coefficient, addressing a common oversight in astronomical data analysis.

Contribution

It presents novel, easily implementable Monte Carlo techniques for error estimation of Spearman's rank correlation, improving reliability in astronomical studies.

Findings

Monte Carlo methods effectively estimate Spearman's correlation uncertainties.

The approach provides detailed probability distributions for correlation coefficients.

Enhanced accuracy in correlation significance assessment in astronomy.

Abstract

Spearman's rank correlation test is commonly used in astronomy to discern whether a set of two variables are correlated or not. Unlike most other quantities quoted in astronomical literature, the Spearman's rank correlation coefficient is generally quoted with no attempt to estimate the errors on its value. This is a practice that would not be accepted for those other quantities, as it is often regarded that an estimate of a quantity without an estimate of its associated uncertainties is meaningless. This manuscript describes a number of easily implemented, Monte Carlo based methods to estimate the uncertainty on the Spearman's rank correlation coefficient, or more precisely to estimate its probability distribution.