Once users have obtained standard errors for the basic estimates, there may be situations where users create derived estimates, such as percentages or differences that also require standard errors.
All methods in this section are approximations
and users should be cautious in using them. This is because these methods do not consider the correlation or covariance between the basic estimates. They may be overestimates or underestimates of the derived estimate's standard error depending on whether the two basic estimates are highly correlated in either the positive or negative direction. As a result, the approximated standard error may not match direct calculations of standard errors or calculations obtained through other methods.
- Sum or Difference of Estimates
As the number of basic estimates involved in the sum or difference increases, the results of this formula become increasingly different from the standard error derived directly from the ACS microdata. Care should be taken to work with the fewest number of basic estimates as possible. If there are estimates involved in the sum that are controlled in the weighting then the approximate standard error can be tremendously different.
Here we define a proportion as a ratio where the numerator is a subset of the denominator, for example the proportion of persons 25 and over with a high school diploma or higher.
If the value under the square root sign is negative, then instead use
If P = 1 then use
If Q = 100% x P (a percent instead of a proportion), then SE(Q) = 100% x SE(P).
If the estimate is a ratio but the numerator is not a subset of the denominator, such as persons per household, per capita income, or percent change, then
For a product of two estimates - for example if users want to estimate a proportion's numerator by multiplying the proportion by its denominator - the standard error can be approximated as
Users may combine these procedures for complicated estimates. For example, if the desired estimate is
then SE(A+B+C) and SE(D+E) can be estimated first, and then those results used to calculate SE(P).
For examples of these formulas, please see any Accuracy of the Data document available on the
ACS website at: http://www.census.gov/programs-surveys/acs/technical-documentation/codelists.html