We frequently find ourselves calculating a statistic like "the population (with a margin of error) earning less than 2.00X the FPL". These fields are found in the C17002 (C17002_001 to C17 C17002_008) family of tables. (data.census.gov/table
Calculating the total number of people whose ratio of income to poverty level is less than 2.00 is straightforward. We can either sum the lower categories (Under 0.50 through 1.85 to 1.99) or subtract the highest category from the total. Either way provides the same value.
However, we also want the margin of error of the estimate. Would it be appropriate to assume the margin of error people earning "less than 2.00 and over" would be equal to "2.00 and over" because they are two complementary pieces of a whole? The alternative is to follow ACS guidance on margins of error for derived estimates. The two routes to the margin of error, as expected, yield different results.
Does anyone have thoughts on how to handle MOEs when you essentially want to collapse a set of census tables into "characteristic" and "not a characteristic"?
You can apply the formulas in chapter 8 for sums (combining categories) for an arbitrary "linear combination" or "weighted sum." The compliment is just the total population - the "other" category. A weighted sum is just a sum with coefficients or "multipliers" such as 1.0 *a +0.3*b - 2*c, etc.
The MOE of a sum is the square root of the sum of the individual MOEs squared. The estimate of the weighted sum is given by the equation above. The MOE of 3*(a) is just 3*MOE.
In R if you have a vector of estimates, a vector of MOEs and a corresponding vector of weights then
weighted.estimate.MOE<-function(est,moe,weights) c(est=sum(est*weights),moe=sqrt(sum((moe*weights)^2))
Note that the universe for Poverty measures is the population for which poverty is determined NOT the total population.
Dave
As a note when I am using poverty measures I create a 3 category variable "Above","Below","Undefined" by subtracting Undefined = Total Pop - Above- Below Here is where the Weighted Sum R function comes into play. The coefficients are 1,-1,-1. Use B01003 to get the total population.