The following article provides a brief primer and overview of multilevel and hierarchical linear modeling. The school-effects model with random effects is illustrated with a heuristic dataset. Finally, recommendations are presented for researchers studying learning disabilities who would like to utilize this methodology.

Three procedures for evaluating the replicability of descriptive discriminant analysis (DDA) results are discussed. The techniques include cross-validation, the jackknife, and the bootstrap. Discriminant analysis is a multivariate technique used when group membership or classification is the focus of the analysis. DDA is used to describe major…

A new method for evaluating model fit that is easy to use and interpret is presented. The new method, which uses a binomial test of the number of hypotheses (paths) in a model that are supported by the data, has heuristic value when considering problems associated with other goodness-of-fit measures. An application of the binomial test as a…

The present paper suggests that multivariate techniques are very important in social science research, and that canonical correlation analysis may be particularly useful. The logic of canonical analysis is explained and discussed. The necessity of using replicability/generalizability analyses is argued. It is suggested that cross-validation…

The use of Procrustean rotation as a procedure for assessing the invariance of study results is proposed. Researchers have long relied on significance testing as a measure of judging the worthiness of empirical findings. However, significance testing has come under fire because it does not provide information about the importance or replicability…

Statistical significance is often inappropriately equated with evaluating result importance and evaluating result replicability, even though these are three somewhat different issues. The prudent researcher must separately assess each of these elements of the "research triumvirate" by using different methods. This paper focuses on two…

Three strategies for augmenting the interpretation of significance test results are illustrated. Determining the most suitable indices to use in evaluating empirical results is a matter of considerable debate among researchers. Researchers increasingly recognize that significance tests are very limited in their potential to inform the…