) / Cramer’s Phi (
) is a measure of association and is like the effect size equivalent for a Chi Squared statistic. Cramer’s Phi is used when the Chi Squared matrix is bigger than a 2 x 2 matrix. The formula is:Phi () / Cramer’s Phi () is a measure of association and is like the effect size equivalent for a Chi Squared statistic. Cramer’s Phi is used when the Chi Squared matrix is bigger than a 2 x 2 matrix. The formula is:
where N = Total number of subjects and K = the smaller of the number of rows or columns.
However, when the matrix is just a 2 x 2 then there is no need to utilize k and the formula comes down to:
Either way, the end result is interpreted like a correlation coefficient (Pearson r). The square of the result, therefore, lets you know how much shared variance is accounted for by the relationship detected by the Chi Squared. Therefore, a Phi of 0.373 would mean that about 13.91% (
) of the variance is accounted for by the relationship measured in the Chi Square.