States in the Regional Educational Laboratory (REL) Central region serve a largely rural population with many states enrolling fewer than 350,000 students. A common challenge identified among REL Central educators is identifying appropriate methods for analyzing data with small samples of students. In particular, members of the REL Central…

Publication selection bias is a serious challenge to the integrity of all empirical sciences. We derive meta-regression approximations to reduce this bias. Our approach employs Taylor polynomial approximations to the conditional mean of a truncated distribution. A quadratic approximation without a linear term, precision-effect estimate with…

The likelihood for generalized linear models with covariate measurement error cannot in general be expressed in closed form, which makes maximum likelihood estimation taxing. A popular alternative is regression calibration which is computationally efficient at the cost of inconsistent estimation. We propose an improved regression calibration…

Used Johnson's transformation (N. Johnson, 1978) with approximate test statistics to test the homogeneity of simple linear regression slopes in the presence of nonnormality and Type I, Type II or complete heteroscedasticity. Computer simulations show that the proposed techniques can control Type I error under various circumstances. (SLD)

This study investigates parameter estimation under the simple linear regression model for situations in which the underlying assumptions of ordinary least squares estimation are untenable. Classical nonparametric estimation methods are directly compared against some robust estimation methods for conditions in which varying degrees of outliers are…

Traditionally, the errors-in-variables problem is concerned with the point estimation of the slope of the true scores regression line when the regressor is measured with error, and when no specification error is present. In this paper, the errors-in-variables problem is extended to include specification error. Least squares procedures provide a…

Ridge estimates (REs) of population beta weights were compared to ordinary least squares (OLS) estimates through computer simulation to evaluate the use of REs in explanatory research. With fixed predictors, there was some question of the consistency of ridge regression, but with random predictors, REs were superior to OLS. (SLD)

The use of stepwise regression has been criticized for both interpretive misunderstandings and statistical aberrations. A major statistical problem with stepwise regression and other procedures that involve multiple significance tests is the inflation of the Type I error rate. General approaches to control the family-wise error rate such as the…

The regression-discontinuity approach to evaluating educational programs is reviewed, and regression-discontinuity post-program mean differences under various conditions are discussed. The regression-discontinuity design is used to determine whether post-program differences exist between an experimental program and a control group. The difference…