This article proposes a flexible extension of the Fay--Herriot model for making inferences from coarsened, group-level achievement data, for example, school-level data consisting of numbers of students falling into various ordinal performance categories. The model builds on the heteroskedastic ordered probit (HETOP) framework advocated by Reardon,…

It is common in regression discontinuity analysis to control for high order (third, fourth, or higher) polynomials of the forcing variable. We argue that estimators for causal effects based on such methods can be misleading, and we recommend researchers do not use them, and instead use estimators based on local linear or quadratic polynomials or…

Students in statistics service courses are frequently exposed to dogmatic approaches for evaluating the role of randomization in statistical designs, and inferential data analysis in experimental, observational and survey studies. In order to provide an overview for understanding the inference process, in this work some key statistical concepts in…

This working paper contains the overheads used in a seminar designed to introduce some basic concepts of statistics to nonstatisticians. The seminar has been presented on several occasions. The first part of the seminar, and the first set of overheads, deals with the essentials of statistics, including: (1) population, sample, and inference; (2)…

P. O. Johnson and J. Neyman (1936) proposed a general linear hypothesis testing procedure for testing the null hypothesis of no treatment difference in the presence of some covariates. This is generally known as the Johnson-Neyman (JN) technique. The need for the hypothesis testing step (often omitted) as originally presented and the…

Often, all of the variables in a model are latent, random, or subject to measurement error, or there is not an obvious dependent variable. When any of these conditions exist, an appropriate method for estimating the linear relationships among the variables is Least Principal Components Analysis. Least Principal Components are robust, consistent,…

Presents two mathematical methods for fitting the logistic curve to population data supplied by the U.S. Census Bureau utilizing computer algebra software to carry out the computations and plot graphs. (JKK)

Statistical significance is misused in educational and psychological research when it is applied as a method to establish the reliability of research results. Other techniques have been developed which can be correctly utilized to establish the generalizability of findings. Methods that do provide such estimates are known as invariance or…

One of the most appropriate quasiexperimental approaches to compensatory education is the regression-discontinuity design. However, it remains underutilized, in part because of the need to clarify the link between the mathematical model and administrative decision-making. This paper explains the derivation of a program efficiency index congruent…