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 19 reports on the average combined science literacy scores of 15-year-old students in 2006. In Australia, the average combined science literacy scores of male and female students were each 527 (see table 19-2). In contrast to the similarity of these scores, the standard errors for these estimates were 3.2 and 2.7, respectively (see table S19-2). The average score with the smaller standard error provides a more reliable approximation of the true value than does the average score with a higher standard error. In addition, 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, writing, and economics scores on the National Assessment of Educational Progress (indicators 12, 13, 14, 15, and 16), 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).