We investigated language variation and score variation in the testing of English language learners, native Spanish speakers. We gave students the same set of National Assessment of Educational Progress mathematics items in both their first language and their second language. We examined the amount of score variation due to the main and interaction…

Written by a social worker for social work students, this is a nuts and bolts guide to statistics that presents complex calculations and concepts in clear, easy-to-understand language. It includes numerous examples, data sets, and issues that students will encounter in social work practice. The first section introduces basic concepts and terms to…

In practical applications of item response theory (IRT), item parameters are usually estimated first from a calibration sample. After treating these estimates as fixed and known, ability parameters are then estimated. However, the statistical inferences based on the estimated abilities can be misleading if the uncertainty of the item parameter…

An abbreviated version of the Social Phobia and Anxiety Inventory (SPAI) was developed using methods based in nonparametric item response theory. Participants included a nonclinical sample of 1,482 undergraduates (52% female, mean age = 19.4 years) as well as a clinical sample of 105 individuals (56% female, mean age = 36.4 years) diagnosed with…

This paper presents an argument against the wider adoption of complex forms of data analysis, using multi-level modeling (MLM) as an extended case study. MLM was devised to overcome some deficiencies in existing datasets, such as the bias caused by clustering. The paper suggests that MLM has an unclear theoretical and empirical basis, has not led…

Univariate latent growth modeling (LGM) of composites of multiple items (e.g., item means or sums) has been frequently used to analyze the growth of latent constructs. This study evaluated whether LGM of composites yields unbiased parameter estimates, standard errors, chi-square statistics, and adequate fit indexes. Furthermore, LGM was compared…

A person fit test based on the Lagrange multiplier test is presented for three item response theory models for polytomous items: the generalized partial credit model, the sequential model, and the graded response model. The test can also be used in the framework of multidimensional ability parameters. It is shown that the Lagrange multiplier…

High quality assessment practice is expected to yield valid and useful score-based interpretations about what the examinees know and are able to do with respect to a defined target domain. Given this assertion, the article presents a framework based on the "unified view of validity," advanced by Cronbach and Messick over two decades ago, to assist…

An equation comparable to Spearman's correction for attenuation, which does not depend upon the assumption that error scores are uncorrelated with true scores and with other sets of scores, is derived. (Editor)

A new formula, expressing relative efficiency solely in terms of the standard errors of measurement and the frequency of distributions of true scores, is developed for the relative efficiency of two tests measuring the same trait. Subtests from the Scholastic Aptitude Test provide a numerical illustration. (Author/RC)

In analyzing exploratory repeated measures data with more than two measures, two competing tests must be administered simultaneously if one is to make an efficient and effective decision regarding the tenability of the null hypothesis of no differences among measurement means. Obviously, such a procedure is not without a cost vis-a-vis Type I…

This Digest presents a discussion of the assumptions of multiple regression that is tailored to the practicing researcher. The focus is on the assumptions of multiple regression that are not robust to violation, and that researchers can deal with if violated. Assumptions of normality, linearity, reliability of measurement, and homoscedasticity are…

The relationship between generalizability and validity is explained, making four important points. The first is that generalizability coefficients provide upper bounds on validity. The second point is that generalization is one step in most interpretive arguments, and therefore, generalizability is a necessary condition for the validity of these…