An exact test for all-way interaction in a 2(M) contingency table: Application to interval capture-recapture estimation of population size

An exact conditional test for an M-way log-linear interaction in a fully ob served 2(M) contingency table is formulated. From this is derived a procedu re for interval estimation of the total count N in a 2(M) contingency table , one of whose entries is unobserved. This procedure has an immediate appli cation to interval estimation of the size of a closed population from incom plete, overlapping lists of records, as in capture-recapture analysis of ep idemiological data. Data on the prevalence of spina bifida in live births i n upstate New York in 1969-1974 illustrate this application.