Calculating a percent of a margin of error

Good morning Elizabeth -
I might propose an entirely different approach -- using population-weighted centroids for the spatial analysis. (What if the entire population is in the 25% of the block group land area that is outside the floodplain?) If the centroid falls within the floodplain, I'd assign the population to the floodplain, if outside, I would exclude the population from the floodplain.

The centroid method, of course, introduces its own kind of potential error, so you could always run the analysis both ways and report a range?

You can find the block group weighted centroids here:
www.census.gov/.../centersofpop.html

There is a formula for combining margins of error. One combines the groups and should generally recompute the standard error, which will be much smaller for larger areas. If the area is smaller than the entire area, the standard error should be higher. In the simplest terms (the Census uses complex sampling for the ACS) the standard error is function of the square root of the total. So if your sample is based upon 100 and the margin of error is 16%, if your sample is based upon 400 the standard error becomes 8%, etc. Complex sampling increases the standard error, by effectively shrinking the sample size by the design effect.