Standard Errors

When data from samples are reported, as is the case with most of the indicators in The Condition of Education, the standard error is calculated for each estimate. The standard errors for all estimated totals, means, medians, or percentages reported in the tables of The Condition of Education can be accessed through links in the analyses and indicators.

The standard errors of the estimates for different subpopulations in an indicator can vary considerably. As an illustration, indicator 18 reports on the adult literacy scores of adults age 16 or older in the United States in 2003. The average quantitative scores of adults who spoke only English and those who spoke English and a language other than Spanish were each 289 (see table 18-1). In contrast to the similarity of these scores, their standard errors were 1.2 and 4.1, respectively (see table S18-1). The average score with the smaller standard error provides a more reliable estimate of the true value than does the average score with a higher standard error. Standard errors tend to diminish in size as the size of the sample (or subsample) increases. Consequently, for the same kinds of data, such as reading, mathematics, and science scores on the National Assessment of Educational Progress (indicators 11, 12, and 13), standard errors will almost always be larger for Blacks and Hispanics than for Whites, who represent a larger proportion of the population.

For indicator 20, which reports median annual earnings, special procedures are followed for computing the standard errors for these medians. See appendix G of the source and accuracy statement for the Current Population Study (CPS) 2006 Annual Social and Economic supplement (ASEC) for information on how to calculate the standard errors (http://www.census.gov/
apsd/techdoc/cps/cpsmar06.pdf).