Phi Coefficient Calculator

Instructions: This calculator computes the value of the Phi Coefficient. Please first indicate the number of columns and rows for the cross tabulation, and then type the table data:

Num. Rows = Num. Cols =   

More about the Phi Coefficient

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).

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.

In case you have any suggestion, or if you would like to report a broken solver/calculator, please do not hesitate to contact us.

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