Variation in Populations

In considering the estimates in the tables and figures shown in this volume and on the NCES website, it is important to keep in mind that there may be considerable variation among the members of a population in the characteristic or variable represented by the population estimate. For example, the estimated average mathematics score of United States 4th-graders in 2007 was 529 (see table A-15-1). In reality, many U.S. students scored above 529 points, and many scored below 529 points. Likewise, not all faculty salaries, benefits, and total compensation at postsecondary institutions were the same at each type of institution in 2007-08 (indicator 43). Because of this variation, there may be considerable overlap among the members of two populations that are being compared. Although the difference in the estimated means of the two populations may be statistically significant, many members of the population with the lower estimated mean may be above the estimated mean of the other population, and vice versa. For example, there may be a percentage of young adults with a high school diploma or equivalent that have higher earnings than young adults with a bachelor's degree or higher (indicator 17). The extent of such overlap is not generally considered in the indicators in this volume. Estimates of the extent of variation in such population characteristics can be computed from the NCES survey datasets or are available in published reports. For example, estimates of the variation in students' assessment scores can be found using the NAEP Data Explorer at http://nces.ed.gov/nationsreportcard/nde/ or in the appendices to most NAEP reports.