Convert a margin of error to a standard error

Divides a margin of error (MOE) by the normal quantile \(z\) for the level, giving the standard error (SE): \(\mathrm{SE} = \mathrm{MOE} / z\). A margin of error is the half-width of a confidence interval. When level is 0.90, the level of published American Community Survey (ACS) margins of error, the function uses \(z = 1.645\), the value the Census Bureau uses. At other levels it uses qnorm(1 - (1 - level) / 2). The function is the inverse of cacs_se_to_moe() at the same level.

Usage

cacs_moe_to_se(moe, level = 0.9)

Arguments

moe

A numeric vector of margins of error.

level

A single number between 0 and 1 (not a percentage) giving the confidence level at which the margins of error were computed. The default is 0.9. The value is not checked: level = 90, for example, gives NaN with a warning.

Value

A numeric vector of standard errors, the same length as moe.

Details

ACS 1-year margins of error for 2005 and earlier were published with \(z = 1.65\); dividing them by 1.65 gives the standard error. The values of moe are not checked. The negative codes that the Census Bureau's data API puts in place of some margins of error, such as -555555555, are divided like any other number and give negative standard errors. cacs_acs_prefetch() returns these codes as NA.

References

U.S. Census Bureau (2020). Understanding and Using American Community Survey Data: What All Data Users Need to Know. Chapter 7, Understanding Error and Determining Statistical Significance.

See also

cacs_propagate_moe() computes margins of error for drive-time area estimates.

Other rates and margins of error: cacs_acs_default_rates, cacs_se_to_moe()

Examples

cacs_moe_to_se(c(8.225, 16.45, NA), level = 0.90)
#> [1]  5 10 NA