This paper addresses statistical aspects of the No Child Left Behind (NCLB) Act, 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, but so far the issue remains unresolved. Here we will discuss in general what a gap might be, provide some additional approaches to estimating gaps, and discuss advantages and disadvantages of each.

Each of the candidate definitions of gap given will be evaluated with respect to three quantitative measures of student performance derived from the National Assessment of Educational Progress (NAEP): mean scale scores, percentage at or above basic achievement level, and percentage at or above proficient achievement level. This evaluation will be done both through a discussion of the statistical properties of the various gap estimators and through comparison of state-level sample sizes computed for each.