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General Cautions About Comparing Estimates

Cautions about comparing direct survey estimates obtained from different surveys

Differences between direct survey estimates obtained from different sources (Census 2000, CPS ASEC, ACS) reflect both differences in the true levels of income and poverty (when comparing estimates for different places or different years), as well as differences in the methods by which the survey data were collected and the estimates were made. The following papers describe these differences between the data sources.

Cautions about comparing SAIPE intercensal model-based county estimates and direct survey estimates

Census 2000 and ACS direct survey estimates are used in construction of the SAIPE model-based estimates of poverty and median household income. Therefore, the intercensal model-based estimates almost certainly exhibit a positive correlation with Census 2000 and ACS direct survey estimates.

When testing the significance of differences in estimates from these sources, caution should be used in deriving the confidence intervals. Although we currently do not have estimates of the individual correlations or advice on estimating the general magnitude of the correlation, failure to incorporate the positive correlation between the estimates will produce confidence intervals that are too wide; thus, too many differences will be considered "not significant." This caution does not apply to comparisons between Census 2000 state-level data because the Census 2000 estimates have close to negligible sampling error.


Cautions about comparing SAIPE model-based estimates for different years

Statistical comparisons of SAIPE state and county estimates across years are possible if cross-year correlations are taken into account. For all years of estimates, there is correlation of the model error, and for the years prior to 2005 there is correlation of the sampling error as well. Methodologies for comparison of state and county estimates have been developed, but currently no methods are available for comparing school district estimates across different years.

For state-level estimates, Methodology for Testing for a Rise in Child Poverty Rate [PDF - 141k] describes a methodology for taking into account these cross-year correlations in estimating if any states have a five percent or greater significant change in child poverty rate between two years.

A methodology for counties has also been developed for use in analyzing trends in poverty over time. This methodology and corresponding results are documented in the Serial Comparisons in Small Domain Models. [PDF - 235k] These methods cannot be applied directly to published estimates, however, since changes to survey coverage, geographic definitions, and SAIPE methodology create breaks in the published time series.

For the series of SAIPE state and county estimates, notable differences include the break between 2004 and 2005 due to the switch from CPS ASEC to ACS data in SAIPE modeling. Comparisons across these particular years are not advised because of this break in series. See Estimation Procedure Changes for the 2005 Estimates for more details. Also, with the introduction of group quarters populations to the ACS starting with the 2006 ACS, comparability for certain age groups across 2005 and 2006 is limited. Generally residents of group quarters have higher poverty rates than residents of households, and this affects the comparison. See ACS 2006 Subject Definitions, pp. 69-73 for more details. Finally, a modification to the methodology for calculating standard errors was made between the 2008 and 2009 estimates, as described in Estimation Procedure Changes for 2006-2009.

As described in Estimation Procedure Changes, the SAIPE 2010 estimates use the recently available decennial 2010 benchmark at all stages of production: state, county and school district. Thus, caution should be used in comparing numbers of individuals in poverty from SAIPE 2010 to previous years, which relied on earlier decennial benchmarks. School district population and poverty estimates, in particular, are not comparable with previous years. Poverty rates for the 2005-09 period should be comparable to SAIPE 2010 poverty rates, however, as all are unbiased estimators with the same list of inputs and model procedure. Cautions about measurement differences cited in previous paragraphs still apply.

Given the comparability of poverty rates for a given domain across this six-year period, comparisons between the estimates for different years are possible for states and counties. Guidance on making these comparisons is given in Guidance for Making Year-to-Year Comparisons.


Cautions about comparing SAIPE model-based estimates for different states or different counties in the same year

All SAIPE model-based estimates are correlated because they depend on the same regression coefficients. Also estimates for individual states are controlled to add up to the national ACS estimate, and counties within each state are controlled to add up to the state-level estimate. These controls create additional correlation. Therefore, to make comparisons between two or more states or counties, it is not sufficient to take the variances (implied by the confidence intervals) for the two different places and apply the usual estimates-difference hypothesis testing. Methodology has been developed for making these comparisons, and some results are reported in the 2009 SAIPE Highlights. [PDF - 2.1M] On average, these correlations are small (less than 5%), but can vary from near zero to over 30%. Due to this wide dispersion in potential correlation, SAIPE does not provide general guidance for comparing arbitrary pairs of states or counties.


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