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Quantifying Uncertainty in State and County Estimates

The model-based estimates almost certainly differ from the figures that would result from administering the American Community Survey (ACS) to all households in the nation. These differences might arise because a sample was surveyed rather than all households, because our model does not fit all counties, or for other reasons. The possibility of these differences creates uncertainty about the estimates. Standard errors are produced for all of the model-based estimates, largely to provide an indication of the overall quality of the set of all county estimates. With some caution they may also be used to provide confidence intervals for individual estimates.

The standard errors represent "uncertainty" arising from several sources, especially:

  • ACS sampling variation within counties; and
  • "lack of fit" of the model to what the ACS measures.

ACS sampling variation creates uncertainty about the model predictions because the direct estimation of variance becomes more precise as county size increases. It is also present but reduced in the shrinkage estimates for counties with ACS sample households. We represent the uncertainty arising from lack of fit of the model as a variance constant over all counties, since we do not know which counties the model doesn't fit. In general, the sampling variance is large compared with the lack of fit variance.

These standard errors are quite different from the estimates of direct sampling variation which characterize the uncertainty of U.S. Census Bureau estimates, both because they include nonsampling variance and because of the way sampling variance influences them. We employ these standard errors to form 90 percent confidence intervals and construct the relative width of the 90 percent confidence interval. We use these relative widths to compare standard errors.

Several sources of uncertainty are not represented in the standard errors, including the following:

  • nonsampling error in the ACS, which comes from:
  • -- inability to obtain information about all cases in the sample;
    -- definitional difficulties;
    -- differences in the interpretation of questions;
    -- respondents' inability or unwillingness to provide correct information;
    -- respondents' inability to recall information;
    -- errors made in data collection, such as the method of collection (paper versus computer assisted), recording or coding the data;
    -- errors made in processing the data;
    -- errors made in estimating values for missing data; and
    -- failure to represent all units with the sample, i.e., undercoverage;
  • differences between the counties that have zero persons in poverty and those counties with at least one person in poverty;
  • differences between counties in the true relationship between the administrative records and what the ACS measures; and
  • errors in the administrative records.

Some of these sources of uncertainty are alluded to elsewhere on this web site, as points of difference among the three sets of estimates: census, ACS, and model-based. While we can give examples of the underlying mechanisms for each, we have not made a quantitative assessment of the uncertainty they contribute to the present estimates.

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Source: U.S. Census Bureau | Small Area Income and Poverty Estimates |  Last Revised: April 29, 2013