Paul W. Holland

The Kernel method of test equating

and Notation.- and Notation.- The Kernel Method of Test Equating: Theory.- Data Collection Designs.- Kernel Equating: Overview, Pre-smoothing, and Estimation of r and s.- Kernel Equating: Continuization and Equating.- Kernel Equating: The SEE and the SEED.- Kernel Equating versus Other Equating Methods.- The Kernel Method of Test Equating: Applications.- The Equivalent-Groups Design.- The Single-Group Design.- The Counterbalanced Design.- The NEAT Design: Chain Equating.- The NEAT Design: Post-Stratification Equating.

Univariate and Bivariate Loglinear Models for Discrete Test Score Distributions

The well-developed theory of exponential families of distributions is applied to the problem of fitting the univariate histograms and discrete bivariate frequency distributions that often arise in the analysis of test scores. These models are powerful tools for many forms of parametric data smoothing and are particularly well-suited to problems in which there is little or no theory to guide a choice of probability models, e.g., smoothing a distribution to eliminate roughness and zero frequencies in order to equate scores from different tests. Attention is given to efficient computation of the maximum likelihood estimates of the parameters using Newtons Method and to computationally efficient methods for obtaining the asymptotic standard errors of the fitted frequencies and proportions. We discuss tools that can be used to diagnose the quality of the fitted frequencies for both the univariate and the bivariate cases. Five examples, using real data, are used to illustrate the methods of this paper.

On "State Education Statistics.".

In January 1984 and again in January 1985, then Secretary of Education Bell released the table “State Education Statistics.” These tables contained a variety of education indicators, among them average SAT or ACT scores for each state. In this paper we examine these scores to see if they can be used for state-by-state comparisons to aid in the evaluation of those educational policies that vary across states. We conclude that statistical adjustment to remove the bias introduced by inappropriate aggregation and self-selection of examinees is not sufficient to insure the validity of the kinds of inferences that are desired.

Evaluating the Missing Data Assumptions of the Chain and Poststratification Equating Methods

The nonequivalent groups with anchor test (NEAT) design, also known as the common-item, nonequivalent groups design (Kolen & Brennan, 2004), is used for equating several operational tests. Two types of observed-score equating methods often used with the NEAT design are chain equating (CE) and poststratification equating (PSE). Here, we consider their nonlinear versions, that is, the frequency-estimation equipercentile method for PSE and the chained equipercentile methods for CE (see Kolen & Brennan, 2004).

Effectiveness of an Individualized Computer-Driven Online Math K-5 Course in Eight California Title I Elementary Schools

Stanford Universitys Education Program for Gifted Youth (EPGY) conducted a randomized-treatment experiment during the 2006–2007 school year to test the efficacy, for Title I students, of the technological and individualized EPGY Kindergarten through Grade 5 Mathematics Course Sequence, modified for the Title I schools. Restricting attention to students who were in the top half of the distribution of correct first-exercise attempts (a measure of work and engagement), we found substantial and statistically significant improvements in the 2007 California Standard Math Tests (CST07) scores compared to those of matched control students. Gains in second grade were larger than those in Grades 3 to 5. Less able students, as measured by their 2006 CST mathematics scores, also had, on average, larger gains.

Causal Counterfactuals in Social Science Research

This article is reproduced from the previous edition, volume 3, pp. 1550–1554,