A Note on the Interpretation of n x 2 Tables

Data are frequently acquired or extracted in the form of a contingency table of two rows and several columns, and it is sometimes necessary to consider the distribution of entries into the various cells in terms of consistency with some hypothesis. Where the ranking order of the columns is of no consequence, the conventional and widely recommended x2 tests may De appropriate, pro vided the totals in the two rows are not grossly disproportionate in number. If they are grossly disproportionate in number tests based on the ratio of the observed to the expected variance on the assumption of a Poisson distribution are more efficient (Berkson, 1940; Cochran, 1954). These cases in which the ranking order of the columns is inconsequential are comparatively rare, except in relation to genetic segregation. Almost always the order of the columns is meaningful, and any test which fails to appreciate this is clearly inefficient. The conventional %2 test of contingency gives a result which is uninfluenced by arranging the columns in any of n ways, and this result is related to n-1 degrees of freedom, only one or two of which are likely to be related to any biologically meaningful variation. In ad dition, it is unrelated to any intuitively meaningful estimator.