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The multiple‐matrix item sampling designs that provide information about population characteristics most efficiently administer too few responses to students to estimate their proficiencies individually. Marginal estimation procedures, which estimate population characteristics directly from item responses, must be employed to realize the benefits of such a sampling design. Numerical approximations of the appropriate marginal estimation procedures for a broad variety of analyses can be obtained by constructing, from the results of a comprehensive extensive marginal solution, files of plausible values of student proficiencies. This article develops the concepts behind plausible values in a simplified setting, sketches their use in the National Assessment of Educational Progress (NAEP), and illustrates the approach with data from the Scholastic Aptitude Test (SA T).

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The availability of high speed computers has not only allowed persons in educational research to perform larger statistical analyses but also to think differently about their problems. The purpose of this thesis is to reexamine the methods of statistical calculus in the light of high speed computers and to present several special matrix operators which are especially useful. These operators are designed for simplicity and efficiency on high speed computers. Using these operators, we explore many different statistical techniques which are commonly used in educational research and show simple computational formulae. We observe that these statistics are computed more simply from the general linear model than from the usual computing procedures. We conclude that persons in educational research and in other areas need to place much more emphasis on mathematical models and much less emphasis on the special techniques which were developed for desk calculators. The introduction to the thesis discusses the present methods of statistical calculus and their disadvantages as procedures for high speed computers. Efficiency on desk calculators and high speed computers is compared, showing that the many ingenious short‐cut procedures developed for desk calculators are quite inefficient for larger machines. Some other approaches to statistical methods for high speed computers are discussed briefly. The thesis contains a review of the statistical background necessary for using the special matrix operators. The form of data and mathematical models is discussed. We present the assumptions which must be made about the error term which is in the model. We also present a summary of well known formulae for many statistics commonly computed in univariate and multivariate analysis. The formulae are given without proof, but the reader is referred to readily available literature in which the proofs are available. The six special matrix operators are discussed in detail. Their mathematical properties are given in the text of the thesis and the details of computing are given in computer subroutines which are listed in Appendix A. The first operator is SCP (sum cross‐products) which is used to compute the known values of normal equations and the various sums of squares and cross‐products which are needed for statistical analysis. This operator may be considered as a subset of the operations performed in computing the product of a matrix pre‐multiplied by its transpose. The second operator is SWP (sweep) which is used to compute the inverse of a subsection of a matrix and to compute partial sums of squares and cross‐products. This operator may be considered as a subset of the operations used in computing an inverse. The TCM (Transform cross‐products matrix) operator is used to transform the cross‐products matrix in a manner equivalent to performing an arbitrary linear transformation of the variables. The remaining three operators are specific transformations of the cross‐products matrix, each being equivalent to a specific transformat...

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Efforts to support children in schools require addressing not only academic issues, but also out-of-school factors that can affect students’ ability to succeed. This study examined academic achievement of students participating in City Connects, a student support intervention operating in high-poverty elementary schools. The sample included 7,948 kindergarten to fifth-grade students in a large urban district during 1999–2009. School- and student-level treatment effects on report card grades and standardized test scores in elementary through middle school were estimated. Propensity score methods accounted for pre-intervention group differences. City Connects students demonstrated higher report card scores than comparisons and scored higher on middle school English language arts and mathematics tests. This study provides evidence for the value of addressing out-of-school factors that impact student learning.

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