Codependence Measures and the Limits of Pearson Correlation

Summary

This introduction defines codependence as a relationship in which information about one random variable helps determine another, while emphasizing that dependence does not establish causality. It presents Pearson correlation as a familiar measure, then explains why it can miss strong nonlinear relationships, such as squared or absolute-value dependence. It also notes that correlation is not a distance metric because it does not meet the defining metric properties.

The module points readers toward alternative measures of codependence and introduces the axioms used to assess whether a measure qualifies as a metric: identity of indiscernibles, symmetry, and the triangle inequality, which together imply non-negativity. The page references presentation materials and a general topology source, but does not itself describe, implement, or compare the alternative methods. Its discussion is conceptual; it offers no financial-market data, empirical results, or guidance on selecting a measure for a particular research task.

Key ideas

• Codependence means that observing one variable can help determine another, but it does not imply causality.
• Pearson correlation measures linear association and can miss nonlinear dependence.
• Correlation does not satisfy the properties required of a distance metric.
• A metric must satisfy identity of indiscernibles, symmetry, and the triangle inequality.
• The introduction points to alternative measures but does not explain or compare them.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.