  The model for homogeneity of proportions in a two-way
contingency-table/cross-tabulation is the same as the model of independence,
except that the probabilistic process generating the data is viewed as fixing
the column totals (but not the row totals). When gauging the consistency of
observed data with the assumption of independence, recent work has illustrated
that the Euclidean/Frobenius/Hilbert-Schmidt distance is often far more
statistically powerful than the classical statistics such as chi-square, the
log-likelihood-ratio (G), the Freeman-Tukey/Hellinger distance, and other
members of the Cressie-Read power-divergence family. The present paper
indicates that the Euclidean/Frobenius/Hilbert-Schmidt distance can be more
powerful for gauging the consistency of observed data with the assumption of
homogeneity, too.
