Confusion when Deriving a Percent and Reporting the Margin of Error

Without knowing what the MOEs actually are for X and Y, the fact that X is a subset of Y (in the case of proportions), we’d expect the MOE(X) to be larger than MOE(Y). So this looks right to me.

Dear David--

This is a huge problem in the ACS.  In the staqndard publicshed numbers, they use the normal approximation to compute the putative standard errro, which they turn into a margin of error.  However, for situations where the percent of given category is small (usually thought of as less than 30%) or large usually though of more than 70%, they still use the normal approximation for the estimate.  This results in some estimates taking on absurd values.  For instance, if they find one person of a given group in the sample they will put out a margin of error that goes below zero, which is obviously absurd if one case was found in a given distribution.  To remedy this they now also report errors based upon random replicates, which are also possible to compute using the PUMS data.  The other approach, which seems to only have been used for so-call Language Determination files is to use Bayesian estimation techniques.  Shortly after they began releasing the ACS I brought this issue to their attention and they responded, eventually saying that it was an important issue and they were trying to figure out how to deal with it in a producation environment.  In a way the Random Replicate approach is the answer.  For your edification, here is the correspondece I had with the Bureau  https://www.dropbox.com/s/lfjo11wm5ma1axx/Memo_Regarding_ACS-With_Response.pdf?dl=0 ;

No, the worked example is correct. X-hat is never-married females (203,119), Y-hat is total females (630,498), MOE(X-hat) is 5,070, and MOE(Y-hat) is 831.

The expression under the square root can be negative.  I which case you use the other formula -- read all the details and footnotes carefully.

Dave Dorer