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…

Propensity score analysis (PSA) is a methodological technique which may correct for selection bias in a quasi-experiment by modeling the selection process using observed covariates. Because logistic regression is well understood by researchers in a variety of fields and easy to implement in a number of popular software packages, it has…

Uses examples of hierarchical linear modeling (HLM) at local and national levels to illustrate proper applications of HLM and dummy variable regression. Raises cautions about the circumstances under which hierarchical data do not need HLM. (SLD)

Consider the nonparametric regression model Y = m(X)+ [tau](X)[epsilon], where X and [epsilon] are independent random variables, [epsilon] has a median of zero and variance [sigma][squared], [tau] is some unknown function used to model heteroscedasticity, and m(X) is an unknown function reflecting some conditional measure of location associated…

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…

An analytic procedure is presented for testing the homogeneity of unstandardized regression weight vectors when the vectors are correlated. The basic design involves repeated measurements on a dependent variable and a set of independent variables. The method is illustrated with a study of perceived leader behavior. (Author/BW)

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…

The purpose of this paper is to illustrate the use of tobit analysis and tobit decomposition in educational research. Tobit estimates of growth rate in the presence of a ceiling effect were compared with ordinary least squares (OLS) and weighted least squares (WLS) estimates. The tobit estimates had the smallest standard error, the smallest bias,…

A method requiring minimal computational effort is presented for transforming ordered residuals for purposes of testing the correctness of a regression model. The method maintains the same logical ordering in the transformed residuals as that of the original residuals and is suitable for either correlated or uncorrelated data. (Author/BS)

The scree test and its linear regression technique are reviewed, and results of its use in factor analysis and Delphi data sets are described. The scree test was originally a visual approach for making judgments about eigenvalues, which considered the relationships of the eigenvalues to one another as well as their actual values. The graph that is…

Various realizations have led to less frequent use of the "OVA" methods (analysis of variance--ANOVA--among others) and to more frequent use of general linear model approaches such as regression. However, too few researchers understand all the various coefficients produced in regression. This paper explains these coefficients and their…

Ordinary least-squares regression treats the variables asymmetrically, designating a dependent variable and one or more independent variables. When it is not obvious how to make this distinction, a researcher may prefer to use orthogonal regression, which treats the variables symmetrically. However, the usual procedure for orthogonal regression is…

Least squares fitting process as a method of data reduction is presented. The general strategy is to consider fitting (linear) models as partitioning data into a fit and residuals. The fit can be parsimoniously represented by a summary of the data. A fit is considered adequate if the residuals are small enough so that manipulating their signs and…

Practical formulas for several analysis of variance (ANOVA) designs and models are presented which make it possible for readers to compute strength of association measures without the use of complete ANOVA tables. (Author/PN)

The use of the Analytic Hierarchy Process (AHP) in assisting researchers to analyze decisions is discussed. The AHP is compared with other decision-analysis techniques, including multiattribute utility measurement, conjoint analysis, and general linear models. Insights that AHP can provide are illustrated with data gathered in an auditing context.…