# Are the MOEs for two mutually exclusive & completely exhaustive percentages equal?

Hello,

A Monday puzzle here:

I am using table B08201 to look at vehicle availability.  The first estimate is total households, and the second estimate is households with no vehicle.  Thanks to the worked examples in the ACS handbooks, I'm able to compute the percentage & associated MOE of households with no vehicle, no problem.

But now I need to calculate the percentage and corresponding MOE of households with a vehicle. The percentage itself is easy. But the MOE of this has me thinking, should the MOE for the percent of households with a vehicle be the same as the one I computed for percent of households with no vehicle? It's still a percentage with the 1st and 2nd estimate of the table. I'm computing it the long way and comparing. It is extremely close for all states, and I'm not sure if these slight differences are being introduced because I'm approximating the MOE for the count of households with a vehicle vs. using the official MOE for the count of households with no vehicle (B08201_002M).

These two percentages (HHs w/ a vehicle & HH w/ no a vehicle) are MECE - Mutually Exclusive, Completely Exhaustive. Meaning, percent of HHs w/ a vehicle = 100 - percent of HHs w/ no vehicle. Would the MOEs of these percentages be the same?

• Have you taken a look at DP04? They have percentages of households with vehicles although they're broken down into several variables by vehicle count. Each percentage variable obviously has a corresponding MOE.

My [very basic] hunch is that the MOEs won't be equal due to the nature of the survey data and statistical methods. I believe I read somewhere that derived MOEs won't be as accurate as ACS-provided MOEs because ACS has access to more data than is publicly available.

• If you try to compute a table from PUMS data that corresponds to a ACS Detail ("B"). Subject (S) or Data Profile (DP) table you should get a larger MoE based on replicate weights since, as you note, the PUMS data is a subset of the full ACS sample.

You can make the replicate weights calculation using the survey package.  You start by creating a function that takes PUMS data and produces a factor variable the has the same categories as the "B" table.  Apply the svymean function to the factor variable and you will get the fraction corresponding to the categories or the svytotal function to get the counts and standard error (SE). the SE can be converted to an MoE -- multiply by 1.645

Dave

• Here is the documentation for the PUMS replicate weights:

https://www.census.gov/content/dam/Census/library/publications/2020/acs/acs_pums_handbook_2020_ch05.pdf

The weighted estimates calculated using the Public
Use Microdata Sample (PUMS) files are estimates
of the entire population. The degree of uncertainty
associated with American Community Survey (ACS)
estimates, known as sampling error, tends to be large
when the sample size is small. Indeed, PUMS estimates
are subject to additional sampling error because the
PUMS data consist of a subsample of the full ACS
sample. Researchers using the PUMS files must calcu-
late their own measures of uncertainty in addition to
producing their own estimates.

The ACS uses replicate weights for the entire sample to compute the MoEs in tables:

Details:

www2.census.gov/.../acs_design_methodology_ch12_2022.pdf