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A Straightforward Approach to Chi-Squared Analysis of Associations in Contingency Tables
In contrast to conventional wisdom that Pearson’s chi-squared at a contingency table is a criterion of statistical independence, rather than a measure of association, this paper establishes operational meaning of the Pearson’s chi-squared as a measure of association. Its normalized version, phi-squared, is the average change of the probability of a category of a feature when a category of the other feature becomes known. Associations between individual categories are captured with Quetelet indexes between them. This allows for operational interpretation of associations between individual categories, which is illustrated at a number of examples from the literature.In contrast to conventional wisdom that Pearson’s chi-squared at a contingency table is a criterion of statistical independence, rather than a measure of association, this paper establishes operational meaning of the Pearson’s chi-squared as a measure of association. Its normalized version, phi-squared, is the average change of the probability of a category of a feature when a category of the other feature becomes known. Associations between individual categories are captured with Quetelet indexes between them. This allows for operational interpretation of associations between individual categories, which is illustrated at a number of examples from the literature.