When calculating derived MOEs for proportions, what is the protocol for when the values inside the square root equal 0? In the examples I’ve found, this is most likely to happen when the numerator and denominator are close to zero and have relatively high MOEs. The resulting MOE when the value inside the square root equals 0 is 0, which seems misleading.

My question is, what is the procedure for handling these cases? If the values equal zero inside the square root, should the calculation be handled differently? Should there be some default assumption for the MOE (i.e. 100% MOE, as shown in the example below)? I’ve been looking through the ACS MOE documentation and haven’t found mention of this particular circumstance.

I am referencing the formula for the MOE of a proportion here: Calculating Measures of Error for Derived Estimates, page 56

And looking at the example of the percent of the population with a disability for American Indian and Alaska Natives, in Census Tract 9820 in Alameda County in Table S1810, ACS 5-Year 2015-2019.

In this example, the AIAN numerator and denominator are both 2, MOEs for both estimates are 3, so my calculation (in R) for the derived MOE is:

`(1/2) * sqrt(3^2 - ((2/2)^2 * 3^2)) `

Which equals 0, while the table on data.census.gov shows the percent MOE as 100%.

I’d appreciate anyone pointing me to documentation that addresses this situation, or any insight on my interpretation of these formulas. Thank you!