5. Conclusions

In summary, we have introduced a direct measure of heterogeneity, , and used it to measure heterogeneity from local area to local area for four variables related to Census coverage. The source of the data is the Census Bureau’s P-12 sample from the 1990 U.S. Census. The heterogeneity we have measured is residual heterogeneity after stratification by age, sex, race and ethnicity, renter-owner status, place-type and broad geographical division of the country. The local areas are units with total populations around 10,000. We find that the area-to-area variance within strata - reflecting geographical heterogeneity - is roughly comparable to the variance from stratum to stratum, even for this fine a stratification.

The variables examined in this study are believed by the Census Bureau to offer meaningful analogues to Census undercount. If this is true, then our results imply that errors due to heterogeneity from local area to local area dominate errors due to sampling variability in the small-area ratio estimation step of the Bureau’s undercount estimates. The errors treated as negligible in the calculation of error margins are larger than the errors included in the calculation. It follows that the Census Bureau’s published margins of error for adjusted Census counts for local areas are likely to be substantial underestimates.

For stratified small-area ratio estimation, our results suggest that the popular “default option” of treating residual heterogeneity as negligible is a serious mistake. When direct measures of error due to heterogeneity are unavailable, a better default option would be to treat residual heterogeneity as being on a par with the variance explained by the stratification factors.

Variables like the P-12 rates can typically vary by 5, 10 or 20 percentage points from local area to local area, even for people of the same age, sex, race, and ethnicity living in communities of the same general size in the same broad areas of the country. In the absence of direct evidence to the contrary, simulation studies of the efficacy of small-area estimation should allow for substantial local heterogeneity. “Diversity” is a byword in America’s political vocabulary. Diversity is certainly the rule, when one looks from place to place across America with the Census Bureau’s 1990 P-12 sample.