We propose a new limited-information goodness of fit test statistic C[subscript 2] for ordinal IRT models. The construction of the new statistic lies formally between the M[subscript 2] statistic of Maydeu-Olivares and Joe (2006), which utilizes first and second order marginal probabilities, and the M*[subscript 2] statistic of Cai and Hansen…

This paper considers the model of school effectiveness (SE) currently dominant in research, policy and practice in England (although the concerns it raises are international). It shows, principally through consideration of initial and propagated error, that SE results cannot be relied upon. By considering the residual difference between the…

Past estimates of the effect of family income on child development have often been plagued by endogeneity and measurement error. In this paper, we use two simulated instrumental variables strategies to estimate the causal effect of income on children's math and reading achievement. Our identification derives from the large, non-linear changes…

Demonstrating good reliability for the difference score in measurement, the results of this study indicate that the difference score is often highly reliable when the correlation between true change and true initial status is nonnegative. In general, when individual differences in true change are appreciable, the difference score shows strong…

This guide is designed to assist those readers of "The Condition of Education" and similar reports who may lack experience or confidence in reading and understanding statistical information. It serves four purposes (1) identifies and describes the principal features of statistical tables and charts; (2) presents a few illustrations of…

Outlines the simple exercise of measuring the length of an object as a concrete paradigm of the entire process of making chemical measurements and treating the resulting data. Discusses the procedure, significant figures, measurement error, spurious data, rejection of results, precision and accuracy, and student responses. (TW)