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For states and counties, comparisons between modeled estimates for two different years, in the 2006-2013 time period are possible for median household income, poverty rate of the all-age population and poverty rate of the population ages 0 to 17. For the school-age poverty rate estimates, which is the population ages 5 to 17 in families, comparisons can be made for a wider interval, 2005-2013. Comparison of the number in poverty for a given period between 2013 and earlier years is not generally recommended. Such comparisons should be done with caution, due to the new decennial 2013 baseline incorporated in the more recent estimates. No guidance for comparison of school district-level estimates, either poverty rates or number in poverty, is given.
The SAIPE program has produced precise estimates of the significance of year-to-year changes for individual counties. Listings for counties in which we measure a significant change at the 90% level over the 2007-2013 interval are given in List of Counties with Significant Changes between 2007 and 2013.xls [XLS - 147k]. For other intervals of interest, an approximate method for determining the significance of changes over time is available.
First, construct an approximate upper bound for the margin of error (MOE) for the difference between the two estimates chosen for comparison. This approximate upper bound MOE is constructed as the square root of the sum-of-squares of the individual MOEs for each estimate (see example below).
If this constructed MOE for the difference is smaller than the absolute value of the calculated difference between the two point estimates, then one can conclude that the two estimates are significantly different for at least a 90% statistical significance level. If the MOE for the difference is larger than the calculated difference between the two point estimates, then the comparison is inconclusive as to whether or not there is a statistically significant difference.
For example, say the 2013 SAIPE estimate for percent in poverty, within the population ages 0-17, were 15.1% for county A, with a MOE of 1.4, and 18.2% in county B, with a MOE of 1.5%. Then the calculation is:
90% MOE for the difference between the two estimates = square-root(1.4 x 1.4 + 1.5 x 1.5) = 2.0% Absolute value of the difference between the two estimates = 18.2 - 15.1 = 3.1%
Since the MOE of the difference, 2.0%, is less than the difference between the two estimates, 3.1%, one can conclude that the two estimates are significantly different, with at least a 90% significance level. In contrast, if county A's poverty rate were instead 16.3%, and all other values as above, then the difference between the two estimates, 1.9%, is less than the MOE of the difference, 2.0%, and the test would be inconclusive.
Note this method produces a reasonable upper bound approximation to the 90% margin of error for the difference, and not an exact MOE. The reason for this caveat is that modeled estimates like SAIPE have correlations between the estimates, and the exact MOE would account for these correlations. For SAIPE over the time period 2005-2013, all correlations have been estimated as strongly positive, which means the exact MOE would be generally smaller than the approximation described above and the recommended test would have a confidence level better than 90%.
The same approximate methodology can be applied to median household income estimates. This technique should only be used for the 2006 to 2013 time period (2005 to 2013 for ages 5 to 17 in families). Earlier SAIPE estimates were based on the Current Population Survey’s Annual Social and Economic Characteristics Supplement, which has a different sample design, period of coverage, and other differences that create a notable difference in poverty and income measurement.