# American Community Survey (ACS): Sampling error

## Four ways of expressing sampling error

1. Margin of Error (MOE)
• Description: "describes the precision of the estimate at a given level of confidence. The confidence level associated with the MOE indicates the likelihood that the sample estimate is within a certain distance (the MOE) from the population value. Confidence levels of 90 percent, 95 percent, and 99 percent are commonly used in practice to lessen the risk associated with an incorrect inference. The MOE provides a concise measure of the precision of the sample estimate in a table [...]."
• Use: Used to compute CI, SE, and CV and to test for statistical significance.
"The Census Bureau encourages you to include the MOE along with the estimate when producing reports, in order to provide the reader with information concerning the uncertainty associated with the estimate."
• Info about computation: The MOE is published along with the ACS estimate and corresponds to a 90% confidence level. (See Compass for alternate confidence levels.)
2. Confidence Interval (CI)
• Description: "The sample estimate and its standard error permit the construction of a confidence interval that represents the degree of uncertainty about the estimate."
• Interpretation: "A 90-percent confidence interval can be interpreted roughly as providing 90 percent certainty that the interval defined by the upper and lower bounds contains the true value of the characteristic."
• Use: "The CI is [...] useful when graphing estimates, to show the extent of sampling error present in the estimates, and for visually comparing estimates."
• Info about computation: The lower bound of the CI is the ACS estimate minus the Margin of Error. The upper bound is the ACS estimate plus the Margin of Error.
A lower bound may be negative. If this does not make sense, set it to zero.
3. Standard Error (SE)
• Description: "a measure of the deviation of a sample estimate from the average of all possible samples."
• Interpretation: "The SE for an estimate depends upon the underlying variability in the population for the characteristic and the sample size used for the survey. In general, the larger the sample size, the smaller the standard error of the estimates produced from the sample. This relationship between sample size and SE is the reason ACS estimates for less populous areas are only published using multiple years of data: to take advantage of the larger sample size that results from aggregating data from more than one year."
• Use: "The SE is [...] used when comparing estimates to determine whether the differences between the estimates can be said to be statistically significant." Also used to compute CV.
• Info about computation: The denominator is 1.65 rather than 1.645 for ACS 1-year estimates for 2005 or earlier.
4. Coefficient of Variation (CV)
• Description: "provides a measure of the relative amount of sampling error that is associated with a sample estimate," a.k.a. the relative standard deviation.
• Interpretation: "The CV is a function of the overall sample size and the size of the population of interest. In general, as the estimation period increases, the sample size increases and therefore the size of the CV decreases. A small CV indicates that the sampling error is small relative to the estimate, and thus the user can be more confident that the estimate is close to the population value."
• Use: "a useful barometer of the stability, and thus the usability of a sample estimate. It can also help a user decide whether a single-year or multiyear estimate should be used for analysis."

Deriving sampling error measures from the published Margin of Error
Margin of Error (MOE) Published along with ACS estimate (EST).
Corresponds to a 90% confidence level. (See Compass for alternate confidence levels.)
Confidence Interval (CI) CI = (EST - MOE, EST + MOE)
Standard Error (SE) SE = MOE / 1.645
Coefficient of Variation (CV) CV = (SE / EST) x 100
(expressed as a percent)

Source: A Compass for Understanding and Using American Community Survey Data: What General Data Users Need to Know, pp. 29-31 and Appendix 3: Measures of Sampling Error, pp. A-11 - A-17.