This paper addresses statistical aspects of the No Child Left Behind (NCLB) Act (Bush, 2001), with the following goals: to further the discussion on how gaps in performance might be defined and to offer candidate gap estimators, to evaluate candidate gap estimators with respect to three separate student performance measures, to provide state-level distributions of major racial and ethnic groups, and to use the obtained state-level race and ethnicity distributions to calculate minimum sample sizes for state-level sampling on federal confirmation tests for each candidate gap estimator and performance measure. The concept of gaps in student performance appears in many places throughout the NCLB Act, especially with respect to gaps in achievement between groups of students considered disadvantaged and not disadvantaged. Unfortunately, the legislation does not provide a statistical definition of a gap, so definition and implementation remains an open question. Notable efforts to clarify the situation have been made (Holland, 2002), but so far the issue remains unresolved. This paper discusses in general what a gap might be, provides some additional approaches to estimating gaps, and discusses advantages and disadvantages of each. The paper is divided into six main sections. Section 2 provides a brief introduction to the Act and describes the statistical aspects of the legislation. How gaps are defined in the Act is described, as well as the related statistic, "adequate yearly progress" (AYP). Section 3 describes how a gap might be defined operationally, gives suggested candidate gap estimators together with their variances, and evaluates their performance in terms of margin of error. Section 4 defines the racial and ethnic groups most likely covered by the Act and uses existing databases to find state-level distributions of these groups. Section 5 identifies state-level sample sizes for the 4th grade NAEP mathematics assessment when the improvement targets can vary by state. Section 6 identifies state-level sample sizes for fixed improvement targets across states. Finally, Section 7 gives conclusions and further recommendations. Includes an appendix. (Contains 8 figures, 24 tables, and 25 footnotes.