One frequently analyzes a subset of the data collected in a survey whe
n interest focuses on individuals in a certain subpopulation of the sa
mpled population. Although it may seem natural to eliminate from the d
ata set all data from individuals outside the subpopulation before ana
lysis, this procedure may yield incorrect standard errors and confiden
ce intervals. The authors give two examples of this using data from th
e 1987 National Health Interview Survey and the 1986 National Mortalit
y Followback Survey. The correct method of analysis is described, as w
ell as a simple condition that, when satisfied, ensures that the elimi
nation approach yields identical answers to the correct method.