# A new correlation coefficient between categorical, ordinal and interval variables with Pearson characteristics

arXiv: https://arxiv.org/abs/1811.11440 · HTML: https://mlsanity.com/paper/1811.11440/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2018.

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## Abstract (arXiv)

A prescription is presented for a new and practical correlation coefficient, φK, based on several refinements to Pearson's hypothesis test of independence of two variables. The combined features of φK form an advantage over existing coefficients. First, it works consistently between categorical, ordinal and interval variables. Second, it captures non-linear dependency. Third, it reverts to the Pearson correlation coefficient in case of a bi-variate normal input distribution. These are useful features when studying the correlation between variables with mixed types. Particular emphasis is paid to the proper evaluation of statistical significance of correlations and to the interpretation of variable relationships in a contingency table, in particular in case of low statistics samples and significant dependencies. Three practical applications are discussed. The presented algorithms are easy to use and available through a public Python library.