Phi Coefficient Calculator

Instructions: You can use this Phi Coefficient calculator by first indicating the number of columns and rows for the cross tabulation, and then inputting the corresponding table data:

Num. Rows = Num. Cols =   

More about this Phi Coefficient Calculator

The Phi Coefficient is a statistic used to measure the strengh of association between two nominal variables, and it take values from 0 to 1. Values close to 0 indicate a weak association between the variables and values close to 1 indicate a strong association between the variables.

The Phi Coefficient \(\phi\) is a symmetric measure, in the sense that it does not matter what variable is placed in the rows and what variable is placed in the columns.

The Phi Coefficient is computed using the following formula:

\[ \phi = \sqrt{ \frac{\chi^2}{n} }\]

where \(n\) corresponds to the total sample size (total number of observations).

What does the phi coefficient measure?

The Phi coefficient is one measure of effect size. Our site provides other effect size calculators, such as the lambda calculator or our gamma calculator , that are used to assess the effect size of the relationship between nominal variables..

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