Carry survey replicates through a derived estimate

Work from a single release

When combining areas or categories, uncertainty depends on how the component estimates move together. Selected five-year ACS tables supply a full-sample estimate and 80 aligned variance replicate estimates. Confirm the table and geographic level are covered and read the release documentation. Do not mix replicate numbers from different releases.

Recreate the statistic before measuring its variation

1. Define the statistic, for example the percentage of an eligible population in two mutually exclusive categories. Write down its numerator and denominator.
2. Compute that percentage from the full-sample columns. Repeat the entire computation within each matching replicate column, including the denominator. If any denominator is zero, investigate; silently dropping that replicate changes the variance procedure.
3. For an ordinary supported estimate, sum the squared differences between each replicate statistic and the full-sample statistic, then multiply by 4/80. Take the square root for the standard error. The multiplier belongs to this design, not every survey with replicate weights.

Hypothetical arithmetic check

Suppose a full-sample percentage is 30. Forty synthetic replicates give 29 and forty give 31. Every squared deviation is one squared percentage point, so the variance is 4, the standard error is 2 points and the approximate 90% margin is 3.29 points. The arithmetic is a check on implementation, not a public estimate.

Use the Census variance methodology, chapter 12 for exceptions involving controlled or zero counts. An all-identical replicate series alone does not establish that the population quantity is known exactly.

Primary source checked 7 November 2026: U.S. Census Bureau: ACS variance replicate tables.

Use this in your study: ACS replicate uncertainty calculator · Download: Survey uncertainty register.