# Efficient algorithms for the sensitivities of the Pearson correlation coefficient and its statistical significance to online data

arXiv: https://arxiv.org/abs/2405.14686 · HTML: https://mlsanity.com/paper/2405.14686/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2024.

## Built on by (most cited first, 1 of 1)

- [Reasoning-based Anomaly Detection Framework: A Real-time, Scalable, and Automated Approach to Anomaly Detection Across Domains](https://mlsanity.com/paper/2510.03486/) (2025)

## Abstract (arXiv)

Reliably measuring the collinearity of bivariate data is crucial in statistics, particularly for time-series analysis or ongoing studies in which incoming observations can significantly impact current collinearity estimates. Leveraging identities from Welford's online algorithm for sample variance, we develop a rigorous theoretical framework for analyzing the maximal change to the Pearson correlation coefficient and its p-value that can be induced by additional data. Further, we show that the resulting optimization problems yield elegant closed-form solutions that can be accurately computed by linear- and constant-time algorithms. Our work not only creates new theoretical avenues for robust correlation measures, but also has broad practical implications for disciplines that span econometrics, operations research, clinical trials, climatology, differential privacy, and bioinformatics. Software implementations of our algorithms in Cython-wrapped C are made available at https://github.com/marc-harary/sensitivity for reproducibility, practical deployment, and future theoretical development.