Chi-Square Tests with One Degree of Freedom; Extensions of the Mantel- Haenszel Procedure
Journal of the American Statistical Association, (1963)Abstract
A published method for analyzing multiple 2 × 2
contingency tables arising in retrospective studies of
disease is extended in application and form. Extensions of
application include comparisons of age-adjusted death
rates, life-table analyses, comparisons of two sets of
quantal dosage-response data, and miscellaneous laboratory
applications as appropriate. Extensions in form involve
considering multiple contingency tables with arbitrarily
many rows and/or columns, where rows and columns are
orderable, and may even be on a continuous scale. The
assignment of some score for each row or column is
essential to use of the method. With scores assigned, a
deviation of the sum of cross products from expectation,
and its variance conditioned on all marginal totals, are
computed for each table and a chi square is determined
corresponding to the grand total of the deviations. For
various specific instances and for various scoring
procedures, the procedure extends or is equivalent to the
asymptotic form of many known nonparametric techniques.