Statistically comparing estimates

Hi All,

I've been doing some research on this and I can't seem to find a clear answer.

I want to use 2014-2019 ACS data to see if there is a statistically significant difference in poverty rates between Cook County and the state of Illinois.  So, I would be comparing Illinois as a whole to a smaller part of Illinois.

I know how to use the Census Bureau's statistical testing tool, but what is the correct method of calculating statistically significant differences?  Is it appropriate to statistically compare two geographic units that overlap a bit?  Or would a better alternative be comparing Cook County to a statewide poverty estimate from which Cook County has been removed?

Any help would be greatly appreciated!

Parents
• I think generally the guidance is just to ignore this covariance, but this could be problematic if the overlap is large.

That said, you could use the Variance Replicate Tables (https://www.census.gov/programs-surveys/acs/data/variance-tables.2019.html) using the B17001 table (poverty table) for State (040) and Counties (050) to create 1+80 poverty rates for Illinois, 1+80 for Cook County, and 1+80 differences. Now you can find the SE of the difference using the successive difference formula.

If you want to do this for each year (not available in replicate table form), you could use variance replicate tables to produce a value for rho:

rho = ( SE(a)^2 + SE(b)^2  - SE(a-b)^2 ) / ( 2 * SE(a) * SE(b) )

and then calculate the SE of the difference using the MOEs in the published tables:

sqrt( SE(c)^2 + SE(d)^2 - 2 * rho * SE(c) * SE(d) )

The assumption here is that the sampling correlation in the one-year estimates is the same as the sampling correlation in the 5-year estimates.

• I think generally the guidance is just to ignore this covariance, but this could be problematic if the overlap is large.

That said, you could use the Variance Replicate Tables (https://www.census.gov/programs-surveys/acs/data/variance-tables.2019.html) using the B17001 table (poverty table) for State (040) and Counties (050) to create 1+80 poverty rates for Illinois, 1+80 for Cook County, and 1+80 differences. Now you can find the SE of the difference using the successive difference formula.

If you want to do this for each year (not available in replicate table form), you could use variance replicate tables to produce a value for rho:

rho = ( SE(a)^2 + SE(b)^2  - SE(a-b)^2 ) / ( 2 * SE(a) * SE(b) )

and then calculate the SE of the difference using the MOEs in the published tables:

sqrt( SE(c)^2 + SE(d)^2 - 2 * rho * SE(c) * SE(d) )

The assumption here is that the sampling correlation in the one-year estimates is the same as the sampling correlation in the 5-year estimates.

Children
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