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…

In this paper, a focus is made on defining processes at stake in an unfamiliar situation coming from discrete mathematics which brings surprising mathematical results. The epistemological framework of Lakatos is questioned and used for the design and the analysis of the situation. The cognitive background of Vergnaud's approach enriches the study…

Studies of group differences in intelligence often invite conclusions about groups in general from studies of group differences in selected populations. The same design is used in the study of group differences in other traits as well. Investigators observe samples from two groups (e.g. men and women) in some accessible population, but seek to…

A major pitfall with fixed-effects analysis of variance in the nested design is illustrated. Under the null hypothesis of no intervention effect, the rejection rate for "F(sub fixed)" in the nested design is greater than the putative Type I error rate of the test, potentially to an extreme degree. (Author/TJH)

Math modeling is currently at the focus of educational methodologists' attention. However, little is known about the extent to which principles of the math modeling lead to methodological fallacies in educational research. The main purpose of this paper is to explore the nature and principles of math modeling and to examine its application in…

A causal model of halo error (HE) is derived. Three hypotheses are formulated to explain findings of negative HE. It is suggested that apparent negative HE may have been misinferred from existing correlational measures of HE, and that positive HE is more prevalent than had previously been thought. (SLD)

Analysis of covariance (ANCOVA) is a data analysis method that is often used to control extraneous sources of variation in non-equivalent group designs. It is commonly believed that as long as the covariate is highly correlated with the dependent variable there is nothing to lose in using ANCOVA, even in non-randomized studies. This paper examines…

Although analysis of covariance (ANCOVA) is used fairly infrequently in published research, the method is used much more frequently in dissertations and in evaluation research. This paper reviews the assumptions that must be met for ANCOVA to yield useful results, and argues that ANCOVA will yield distorted and inaccurate results when these…

The partial correlation coefficient is derived analytically under exemplary factor patterns. In these patterns, variables are described as an additive composition of a set of orthogonal factors, including general, common, and specific factors. Viewed in this framework, it is evident that the partial correlation may yield spurious results.…

The analysis of covariance as a procedure for statistical correction of the effects for an extraneous variable, called a "covariate," is presented. An heuristic data set is used to make the discussion of the calculation of ANCOVA partitions easier to follow. A discussion of homogeneity of regression as an essential condition to be met…

This repeated measures factorial design study compared the results of two procedures for identifying multivariate outliers under varying conditions, the Mahalanobis distance and the Andrews-Pregibon statistic. Results were analyzed for the total number of outliers identified and number of false outliers identified. Simulated data were limited to…

Problems in the measurement of latent variables (LVs) in structural equations causal models are presented, with examples from recent empirical studies. Main issues addressed are (1) two general types of increased operative variables; (2) criteria for indicators of LVs; and (3) disattenuation effects in LV models. (SLD)

To determine if the observed correlation between two variables can be "explained" by a third variable, a significance test on the partial correlation coefficient is often used. This can be misleading when the third variable is measured with error. This article shows how the problem can be partially overcome. (Author/BW)

The use of analysis of variance was examined under the assumption that the treatment had been randomly assigned to students, when in fact, the class had been the unit. Data support the idea that if one can randomly assign treatments to intact classes, consideration should certainly be given to doing so. (Author/GK)

A methodology for determining the optimal number of observations to use in a measurement design when resource constraints are imposed is presented. Two- and three-facet designs are outlined. Parallel closed form formulae can easily be determined for other designs. (TJH)