A CAUTIONARY NOTE ON APPLYING SCORES IN STRATIFIED DATA

When rank tests are used to analyze stratified data, three methods for assigning scores to the observations have been proposed: (S) independ ently within each stratum (see Lehmann, 1975, Nonparametrics: Statisti cal Methods Based on Ranks; San Francisco: Holden-Day); (A) after alig ning the observations within each stratum and then pooling the aligned observations (Hedges and Lehmann, 1962, Annals of Mathematical Statis tics 33, 482-497); and (P) after pooling the observations across ail s trata (that is, without alignment) (Mantel, 1963, Journal of the Ameri can Statistical Association 58, 690-700; Mantel and Ciminera, 1979, Ca ncer Research 39, 4308-4315). Test statistics are formed for each meth od by combining the stratum-specific linear rank tests using the assig ned scores. We show that method P is sensitive to the score function u sed in the case of two moderately sized strata. In general, we recomme nd methods S and A for use with moderate to large-sized strata.