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Contribution Analysis equation

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I was just reading through the Adobe docs regarding contribution analysis and I noticed an "anomaly" (irony intended) in the formula used to calculate Carmer's V stat.

In the above formula, degrees of freedom has not been accounted for. Given that (C+A) represents the entire dataset, subtracting degrees of freedom from rows and columns is required to account for the constraints that arose in using this data.

I'm assuming that this what the below formula is achieving, however, it's unclear.

Thanks for your help.

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