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Phi_K is a practical correlation constant that works consistently between categorical, ordinal and interval variables.
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It is based on several refinements to Pearson's hypothesis test of independence of two variables.
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It is based on several refinements to Pearson's hypothesis test of independence of two variables. Essentially, the
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contingency test statistic of two variables is interpreted as coming from a rotated bi-variate normal distribution,
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where the tilt is interpreted as Phi_K.
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The combined features of Phi_K form an advantage over existing coefficients. First, it works consistently between categorical, ordinal and interval variables.
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Second, it captures non-linear dependency. Third, it reverts to the Pearson correlation coefficient in case of a bi-variate normal input distribution.
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These are useful features when studying the correlation matrix of variables with mixed types.
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The presented algorithms are easy to use and available through this public Python library: the correlation analyzer package.
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Emphasis is paid to the proper evaluation of statistical significance of correlations and to the interpretation of variable relationships
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For details on the methodology behind the calculations, please see our publication. Emphasis is paid to the proper evaluation of statistical significance of correlations and to the interpretation of variable relationships
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in a contingency table, in particular in case of low statistics samples.
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The presented algorithms are easy to use and available through this public Python library.
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For example, the Phi_K correlation analyzer package has been used to study surveys, insurance claims, correlograms, etc.
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For details on the methodology behind the calculations, please see our publication.
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