Calculating margins of error (MOEs)

If you are downloading a table from the Census Bureau, you won’t need to calculate MOEs, they provide them. However, there are at least two instances in which you may need to derive your own: if you are combining ACS estimates or if you are using Census microdata.

Deriving MOEs for aggregations (combining Census-provided MOEs)

If you are aggregating estimates (adding two groups together or adding up geographies into a region the census doesn’t have), you’ll need to calculate margins of error on the new estimates. There are two ways to calculate these MOEs.

• Approximating the margin of error

  • If you are adding a lot of categories or geographies, this approximation method may become less precise because it doesn’t take covariance into account.

  • Doesn’t take covariance into account.

  • In particular, if you are aggregating a lot of zeros (perhaps adding up a small population over multiple geographies), this approximation method isn’t advised because of how the MOEs are calculated for zero estimates.

  • We would recommend doing this in R, and this approximation is built into the tidycensus package.

• Successive Difference Replication Method to calculate MOEs using Variance Reference Tables (VREs)

  • This method calculates MOEs – it isn’t an estimate like the other method.

  • These are the most reliable MOEs for aggregations.

  • Only the ~100 tables have VRE tables released, not all tables.

  • To learn how to do this, watch this webinar.

If you are calculating your own estimates and MOEs (not using out of the box census tables), you will need to apply the CV thresholds to understand reliability and potentially suppress unreliable estimates (those with a CV above .3).

Calculating MOEs for Microdata

If you are using microdata, you will need to calculate margins of error. The easiest and best way to do this is to use R, specifically the tidycensus and srvyr packages. Learn how to do this in this online book on using R for Census data.