Email, response to PolitiFact Texas, Wes Basel, chief, Small Area Estimates Branch, U.S. Census Bureau, Feb. 25, 2013 (received via bureau spokesman Robert Bernstein)

(Commenting on critique offered to PolitiFact Texas by Eva DeLuna Castro of the Center for Public Policy Priorities)

First a clarification.  The post-WWII decennial censuses have not had 100% counts of population income. The poverty estimates from Dec2000 are sample-based, so they have standard errors as well.  And this survey was replaced by the ACS for 2010.

Beyond that, you're basic conclusion is accurate.  The 2011-2010 difference in SAIPE all-age poverty rate for Travis County is not large enough to be statistically significant.  However, your analysis when applied to the rest of the time series and comparisons is somewhat conservative, in that the guidance we provide on comparisions will provide tighter confidence bands than the overlapping confidence intervals test.  (http://www.census.gov/did/www/saipe/methods/yrtoyrcomparison.html)

The overlapping confidence intervals test basically puts an upper bound on the C.I. of the difference,

  MOE difference <= (MOE estimate 1) + (MOE estimate 2)

But since the correlation between SAIPE estimates is overwhelmingly positive, we can put a smaller upper bound, namely

  MOE difference <= sqrt((MOE estimate 1)^2 + (MOE estimate 2)^2)

Example from Travis County 07-11 Time series

        SAIPE All-age Pov (MOE)          Chg from Yr ago           Upper bound for MOE

                                                                           using overlapping CI        Using SAIPE guidance

2007      14.6  (0.85)                    

2008      14.4  (1.05)                      -0.2                       1.9                          1.35

2009      16.0  (0.95)                      +1.6                       2.0                          1.4

2010      18.8  (1.00)                      +2.8                       2.0                          1.4

2011      18.1  (1.10)                      -0.7                       2.1                          1.5

So under the overlapping CI test, only the 2010 to 2009 change is significant.  With the more accurate SAIPE guidance, the 2009 to 2008 change is also significantly greater than zero.

In summary,

1) Decennial-year poverty estimates are based on surveys.  They also have uncertainty and thus confidence intervals.

2) The change in the 2010 to 2011 SAIPE all-age poverty estimate for Travis County is too small to conclude it is significant.

3) Comparing 2011 with any earlier year, (2005-2009), one can conclude the change is significantly greater than zero.  So any time horizon of analysis beyond one year, you can say poverty is higher.

4) For any year, 2005 through 2011, you can use the same statistical procedure to conclude that Travis County all-age poverty rate is higher than the U.S. poverty rate.

5) Much caution must be used for estimates prior to 2005.  Both the U.S. and SAIPE county estimates are CPS based, and thus confidence intervals are a lot wider.  For example, the SAIPE estimate for Travis County in 2004 is 1.6 %age points higher than the U.S., the same gap as in 2007.  The MOE for SAIPE county estimates is more than 3x higher in 2004, however.  So one can make no statitistically accurate conclusion for this year, or any other prior to 2005.

Wes Basel

Small Area Estimates Branch

US Census Bureau