Calculate MOE on aggregate percentages

Hi Joanna,

I emailed acso.users.support@census.gov with a similar question and received this response:
"Are you adding the percentages from 2 categories where all the categories sum to 100% (for example, for a geography, adding the percent under the age of 18 and percent age 18 to 64)? You should be able to add the percents together and then use the approximate MOE formula for a sum (see the Instructions for Statistical Testing, located here: www.census.gov/.../code-lists.html).

If you are adding something like the percent under 18 for county A and the percent under 18 for county B, then you will have to approximate the MOE (as well as the percent) in 2 steps. Find the numerators and denominators, and then approximate the MOE for the numerator as well as for the denominator. Then, as step 2, use the approximation formula for percents."

Is this helpful?

Hi Joanna,

I emailed acso.users.support@census.gov with a similar question and received this response:
"Are you adding the percentages from 2 categories where all the categories sum to 100% (for example, for a geography, adding the percent under the age of 18 and percent age 18 to 64)? You should be able to add the percents together and then use the approximate MOE formula for a sum (see the Instructions for Statistical Testing, located here: www.census.gov/.../code-lists.html).

If you are adding something like the percent under 18 for county A and the percent under 18 for county B, then you will have to approximate the MOE (as well as the percent) in 2 steps. Find the numerators and denominators, and then approximate the MOE for the numerator as well as for the denominator. Then, as step 2, use the approximation formula for percents."

Is this helpful?

Thank you for the reply.

I am adding percentages from 2 categories where each category sums to 100% (e.g., education level of all males 25+ yrs old). I'm confused by the rest of what you said. Just to be clear, I understand to add the percent estimates together to get the total estimate for the new level I created, but it sounds like you are saying to get the new aggregate MOE percentage estimate I add the 2 MOE percentages together then use the " approximate MOE formula for a sum" I didn't see that in the Instructions for Statistical Testing. I saw approximating the SE, but I didn't see how to get the MOE - am I just not seeing it?

Page A-14 in this publication might be helpful to you: www.census.gov/.../ACSGeneralHandbook.pdf

I read through most of this appendix prior to publishing my question. This talks about counts, not proportions. When it talks about proportions it talks about "derived" proportions. The proportions I have I did not derive, they were given, thus I don't have the numerator (I do have the denominator). Sure, I could estimate the numerator by multiplying the percent times the denominator/total population and go at it that way, I just thought there might be a better way.

Is it crazy to simply do the same equation as you would with count data? That is, square the percent MOEs of the 2 percent estimates, sum those 2 squared MOEs and then take the square root of that sum?

Could you consider a percentage to be a proportion, with the percent figure as the numerator and 100 as the denominator?

Perfect! I can to that! (and probably should have thought of that). thanks for all the help, both of you, Glenn and Miriam! sorry I couldn't grasp what Miriam was proposing, still very new to this :)