Comparison of Family Sizes: A Problem from the 1941 Canadian Census

Most of the numerous studies of differential fertility are based either on census or vital registration records which are substantially complete or on large portions of a population which are considered as samples. Before the nature of sampling error was understood it seemed dangerous to base conclusions on a small number of cases, but this need no longer be the case. Small samples may make possible investigations which avoid the limitations of census tables in which only a few variables can be cross-tabulated. In any serious attempt to study the effect of a particular variable, freed from the effects of other relevant variables, at least ten directions of simultaneous cross-classification are required rather than the three or four which are the maximum usually given in a census.