Iso‐chi‐squared testing of 2 × k : ordered tables

The Pearson chi‐squared statistic for testing the equality of two multinomial populations when the categories are nominal is much less appropriate for ordinal categories. Test statistics typically used in this context are based on scorings of the ordinal levels, but the results of these tests are highly dependent on the choice of scores. The authors propose a test which naturally modifies the Pearson chi‐squared statistic to incorporate the ordinal information. The proposed test statistic does not depend on the scores and under the null hypothesis of equality of populations, it is asymptotically equivalent to the likelihood ratio test against the alternative of two‐sided likelihood ratio ordering.