Language programs need multiple test forms for secure administrations and effective placement decisions, but can they have confidence that scores on alternate test forms have the same meaning? In large-scale testing programs, various equating methods are available to ensure the comparability of forms. The choice of equating method is informed by…

In this study, I investigated 2 procedures intended to create test-taker groups of equal ability by poststratifying on a composite variable created from demographic information. In one procedure, the stratifying variable was the composite variable that best predicted the test score. In the other procedure, the stratifying variable was the…

The purpose of this study was to evaluate the combined effects of reduced equating sample size and shortened anchor test length on item response theory (IRT)-based linking and equating results. Data from two independent operational forms of a large-scale testing program were used to establish the baseline results for evaluating the results from…

This article proposes that sampling design effects have potentially huge unrecognized impacts on the results reported by large-scale district and state assessments in the United States. When design effects are unrecognized and unaccounted for they lead to underestimating the sampling error in item and test statistics. Underestimating the sampling…

This technical report provides detailed information regarding the technical, statistical, and measurement attributes of the New York State Testing Program (NYSTP) for the Grades 3-8 Common Core English Language Arts (ELA) and Mathematics 2016 Operational Tests. This report includes information about test content and test development, item (i.e.,…

After many equatings have been conducted in a testing program, equating errors can accumulate to a degree that is not negligible compared to the standard error of measurement. In this paper, the author investigates the asymptotic accumulative standard error of equating (ASEE) for linear equating methods, including chained linear, Tucker, and…

This technical report provides detailed information regarding the technical, statistical, and measurement attributes of the New York State Testing Program (NYSTP) for the Grades 3-8 Common Core English Language Arts (ELA) and Mathematics 2015 Operational Tests. This report includes information about test content and test development, item (i.e.,…

Sampling errors limit the accuracy with which forms can be linked. Limitations on accuracy are especially important in testing programs in which a very large number of forms are employed. Standard inequalities in mathematical statistics may be used to establish lower bounds on the achievable inking accuracy. To illustrate results, a variety of…

This technical report provides detailed information regarding the technical, statistical, and measurement attributes of the New York State Testing Program (NYSTP) for the Grades 3-8 Common Core English Language Arts (ELA) and Mathematics 2014 Operational Tests. This report includes information about test content and test development, item (i.e.,…

In large-scale assessments, such as state-wide testing programs, national sample-based assessments, and international comparative studies, there are many steps involved in the measurement and reporting of student achievement. There are always sources of inaccuracies in each of the steps. It is of interest to identify the source and magnitude of…

Large sample standard errors for the Tucker method of linear equating under the common item nonrandom groups design are derived under normality assumptions as well as under less restrictive assumptions. Standard errors of Tucker equating are estimated using the bootstrap method described by Efron. The results from different methods are compared…

An asymptotic expression for the reliability of a linearly equated test is developed using normal theory. Reliability is expressed as the product of test reliability before equating and an adjustment term that is a function of the sample sizes used to estimate the linear equating transformation. The approach is illustrated. (SLD)

The Maryland Functional Testing Program (MFTP) uses the Rasch model as the statistical framework for the analysis of test items and scores. This paper is designed to assist the reader in developing an understanding of the fit statistics in the Rasch model. Background materials on application of the Rasch model in statistical analysis of the MFTP…

This paper is the first of a series that will compare estimates of error that arises when state assessments are linked to the National Assessment of Educational Progress (NAEP). Different forms of linkage are discussed. Comparisons are made between whole-sample regression, repeated half-sample replication, bootstrap, and jackknife estimates of the…

An attempt was made to evaluate the standard error of equating (at the mean of the scores) in an ongoing testing program. The interest in estimating the empirical standard error of equating is occasioned by some discomfort with the error normally reported for test scores. Data used for this evaluation came from the Admissions Testing Program of…