I have geospacially clipped census blocks into a new geography to estimate the population for the new area (new area/old area * population estimate).
Is there a method to calculate the new margin of error for these new estimates?
To calculate margins of error for derrived estimates (such as when you group across geographies) see Chapter 8 of the Handbook
It provides formulas and examples.
Hope that is helpful.
It seems like Chapter 8 of the handbook deals with aggregating whole geographies (unless I'm reading it wrong) and it seems like OP is wanting to aggregate whole geographies and some 'clipped' or partial geographies. Am I correct in thinking that if it's not included in the handbook, then it's not recommended to work with partial tracts / geographies?
I don't think the handbook--by this omission--is intentionally trying to comment on the appropriateness of working with partial geographies. More to the point, the statistical principles guiding how to adjust MOEs when aggregating whole units are straightforward and easy to specify. The principles guiding MOEs for partial units are entirely unsettled. I took a stab at this issue, indirectly, in this 2007 paper. I don't know of much other research on this specific subject. In short, it depends on exactly how you're disaggregating from the whole to the parts, and the simplest approaches tend to be highly error-prone, so the MOE will tend to grow much larger than if you stick to whole units. Using partial units may still be adequately accurate for many applications, but to my knowledge, no existing literature or formulae will tell you exactly how to determine that.
Ah! Gotcha. Somehow I missed the "clipped" part and assumed they were doing point-in-polygon (whole block). The issues with using partial blocks are FAR greater than those of aggregating MOE. Population and housing are rarely distributed evenly within a block.