Test a difference between two independent ACS estimates

Start with a comparable contrast

Write down the direction of subtraction. Verify that both cells have the same units, universe, period length and confidence level. For percentages, report the difference in percentage points. Comparing a city with its containing county violates the independent-estimates assumption; so can comparing overlapping collection periods. If covariance is relevant, seek aligned replicate estimates or appropriate design information.

Calculate one interval for the difference

For two independent estimates with published 90% margins of error, the approximate 90% margin for their difference is the square root of the sum of the two squared margins. Both input margins must be ordinary numeric sampling margins. A suppression symbol or controlled-estimate annotation is not a measured zero. This approximation excludes nonsampling errors.

Hypothetical comparison

Two disjoint areas have estimated prevalences of 22% and 16%, with 90% margins of 3 and 4 percentage points. The difference is 6 points; its approximate margin is 5, giving an interval from 1 to 11 points. The separate intervals, 19–25 and 12–20, overlap slightly. Judging the contrast from that overlap alone would miss the result of testing the difference.

In a report, state the two underlying estimates, the signed difference, its interval and the independence assumption. A difference compatible with zero does not establish equality. If you searched hundreds of areas for the largest contrast, label it exploratory; this one comparison does not correct for that search.

Primary source checked 7 November 2026: U.S. Census Bureau: ACS statistical testing spreadsheet.

Use this in your study: Independent survey estimate difference.