Generalized phi coefficient ($\varphi =\sqrt{X^2/n}$)

For a contingency table with Pearson chi-squared statistic $X^2$ and sample size $n>0$, the nonnegative magnitude $\varphi =\sqrt{X^2/n}$ is sometimes reported as generalized phi. It does not encode an ordinal direction. In a two-row or two-column table it coincides with Cramér's V; in larger tables it can exceed one, so the normalization in Cramér's V matters. In a two-by-two table it is the absolute value of the Pearson correlation coefficient of binary category indicators; a signed binary phi requires a stated coding convention.