A Comparison of Function-Based Differential Reinforcement Interventions for Children Engaging in Disruptive Classroom Behavior

This study provides a direct comparison of differential reinforcement of other behavior (DRO) and differential reinforcement of alternative behavior (DRA). Participants included three children in center-based classrooms referred for functional assessments due to disruptive classroom behavior. Functional assessments included interviews and brief functional analyses. An alternating treatments design was used to evaluate the relative effectiveness of function-based DRO and DRA interventions. Results indicated that both intervention procedures effectively reduced disruptive behavior, but the DRA procedure consistently resulted in greater reductions in disruptive behavior across all participants. Results are discussed in terms of directions for future functional assessment and intervention research as well as implications for applied practice.     

Peer Tutoring for Reading Fluency as a Feasible and Effective Alternative in Response to Intervention Systems

Peer tutoring is an evidence-based procedure for improving academic performance for a variety of skill areas. The current study evaluated the feasibility and impact of a peer tutoring package for reading fluency with 4 middle school students receiving Tier II remedial supports. This study used a multiple baseline design across participants to evaluate impact of the peer tutoring procedure on students’ oral reading rate on instructional passages. Results indicated that students’ oral reading rate on instructional probes increased following implementation of the peer tutoring procedure. Moreover, peer tutors implemented most steps of the procedure with a high degree of integrity. Results are discussed in terms of contributions to the peer tutoring and Response to Intervention literatures, as well as application to applied practice.     

Split-half and parallel reliabilities of the Purdue Pharmacist Directive Guidance Scale

Using R and SPSS, various forms of split-half and parallel reliabilities were calculated. Robust split-half and parallel reliability coefficients for the Purdue Pharmacist Directive Guidance Scale are presented with coefficients greater than .84.     

Limited Information Goodness-of-fit Testing in Multidimensional Contingency Tables

We introduce a family of goodness-of-fit statistics for testing composite null hypotheses in multidimensional contingency tables. These statistics are quadratic forms in marginal residuals up to order r. They are asymptotically chi-square under the null hypothesis when parameters are estimated using any asymptotically normal consistent estimator. For a widely used item response model, when r is small and multidimensional tables are sparse, the proposed statistics have accurate empirical Type I errors, unlike Pearson's X ². For this model in nonsparse situations, the proposed statistics are also more powerful than X ². In addition, the proposed statistics are asymptotically chi-square when applied to subtables, and can be used for a piecewise goodness-of-fit assessment to determine the source of misfit in poorly fitting models. This research has been supported by the Department of Universities, Research, and Information Society (DURSI) of the Catalan Government, by grant BSO2003-08507 of the Spanish Ministry of Science and Technology, and an NSERC Canada grant. We are grateful to the referees for comments leading to improvements.     

On the asymptotic distribution of Pearson’s X 2 in cross-validation samples

In categorical data analysis, two-sample cross-validation is used not only for model selection but also to obtain a realistic impression of the overall predictive effectiveness of the model. The latter is of particular importance in the case of highly parametrized models capable of capturing every idiosyncracy of the calibrating sample. We show that for maximum likelihood estimators or other asymptotically efficient estimators Pearson's X ² is not asymptotically chi-square in the two-sample cross-validation framework due to extra variability induced by using different samples for estimation and goodness-of-fit testing. We propose an alternative test statistic, X _xval ², obtained as a modification of X ² which is asymptotically chi-square with C−1 degrees of freedom in cross-validation samples. Stochastically, X _xval ² ≤ X ². Furthermore, the use of X ² instead of X _xval ² with a χ _C −1² reference distribution may provide an unduly poor impression of fit of the model in the cross-validation sample. This paper is dedicated to the memory of Michael V. Levine. Requests for reprints should be sent to Albert Maydeu-Olivares, Faculty of Psychology, University of Barcelona, P. Valle de Hebrón, 171, 0835 Barcelona, Spain.