Using Excel for White's Test—An Important Technique for Evaluating the Equality of Variance Assumption and Model Specification in a Regression Analysis

There is consensus in the statistical literature that severe departures from its assumptions invalidate the use of regression modeling for purposes of inference. The assumptions of regression modeling are usually evaluated subjectively through visual, graphic displays in a residual analysis but such an approach, taken alone, may be insufficient for assessing the appropriateness of the fitted model. Here, an easy‐to‐use test of the assumption of equal variance (i.e., homoscedasticity) as well as model specification is provided. Given the importance of the equal‐variance assumption (i.e., if uncorrected, severe violations preclude the use of statistical inference and moderate violations result in a loss of statistical power) and given the fact that, if uncorrected, a misspecified or underspecified model could invalidate an entire study, the test developed by Halbert White in 1980 is recommended for supplementing a graphic residual analysis when teaching regression modeling to business students at both the undergraduate and graduate levels. Using this confirmatory approach to supplement a traditional residual analysis has value because students often find that graphic displays are too subjective for determining what constitutes severe from moderate departures from the equal variance assumption or for assessing patterns in plots that might indicate model misspecification or underspecification.     

“The Coat Traps All Your Body Heat”: Heterogeneity as Fundamental to Learning

This article explores heterogeneity as fundamental to learning. Inspired by Bakhtin's notion of heteroglossia, a design team consisting of an experienced classroom teacher and 2 researchers investigated how a class of 3rd and 4th graders came to understand disciplinary points of view on heat, heat transfer, and the particulate nature of matter. Through a series of planned and unplanned encounters, official versions of the Second Law of Thermodynamics and the particulate view of matter were juxtaposed with varied domains of experience of heat transfer and phase change in water. We analyze the children's discourse to examine how they populated these phenomena with meaning and what they learned in the process. We conclude by describing key principles and a conundrum that emerged from this research.     

A Multidimensional Assessment of Teachers’ Knowledge of Algebra for Teaching: Developing an Instrument and Supporting Valid Inferences

Numerous researchers have suggested that there are multiple mathematical knowledge and skill areas needed by teachers in order for them to be effective teachers of mathematics: knowledge of the mathematics that are the goals of instruction, advanced mathematics beyond the instructional material, and mathematical knowledge that is specific to what is needed to teach students. The research reported here is about the development of a test of teachers’ knowledge in these three areas related to the teaching of algebra. The test development process is described and the results of several analyses are reported that had the goal of checking whether valid inferences can be made about the hypothesized components of teacher knowledge.     

Contrasting State-of-the-Art in the Machine Scoring of Short-Form Constructed Responses

This study compared short-form constructed responses evaluated by both human raters and machine scoring algorithms. The context was a public competition on which both public competitors and commercial vendors vied to develop machine scoring algorithms that would match or exceed the performance of operational human raters in a summative high-stakes testing environment. Data (N = 25,683) were drawn from three different states, employed 10 different prompts, and were drawn from two different secondary grade levels. Samples ranging in size from 2,130 to 2,999 were randomly selected from the data sets provided by the states and then randomly divided into three sets: a training set, a test set, and a validation set. Machine performance on all of the agreement measures failed to match that of the human raters. The current study concluded with recommendations on steps that might improve machine-scoring algorithms before they can be used in any operational way.     

Gender and Ethnicity Among Community College Students: The Relationship Between Adlerian Themes

This study explored the relationship between Adlerian themes, gender, and ethnicity. Results indicate significant differences between Hispanic and Caucasian (non-Hispanic) community college students in Belonging and Social Interest as measured by the BASIS-A. Differences between males and females in Going Along and Wanting Recognition are also explored. The findings are discussed in relation to college students, teaching, and classroom climates.     

BOOK REVIEW

This investigation addressed the effects of teaching styles, student cognitive styles, matched and mismatched conditions, student age, and student gender in relation to course grades in community college education. The Gregorc Style Delineator was used to determine the dominant cognitive styles of 16 teachers and 207 students on two campuses of a comprehensive community college. Data were analyzed according to two analysis of variance models. The findings indicated that concrete sequential teachers assigned significantly lower grades to students than did teachers dominant in any other style and that students 25 years of age and older received significantly higher grades than younger students, except when matched with concrete random teachers. Although many authors have suggested that students whose cognitive styles match those of their teachers tend to attain higher grades, findings in this study contradicted the literature and indicated that mismatched students performed better academically.     

Sustaining High-Quality Teaching and Evidence-Based Curricula: Follow-Up Assessment of Teachers in the REDI Project

Research Findings: Recent research has validated the power of evidence-based preschool interventions to improve teaching quality and promote child school readiness when implemented in the context of research trials. However, very rarely are follow-up assessments conducted with teachers in order to evaluate the maintenance of improved teaching quality or sustained use of evidence-based curriculum components after the intervention trial. In the current study, we collected follow-up assessments of teachers 1 year after their involvement in the REDI (REsearch-based, Developmentally Informed) research trial to evaluate the extent to which intervention teachers continued to implement the REDI curriculum components with high quality and to explore possible preintervention predictors of sustained implementation. In addition, we conducted classroom observations to determine whether general improvements in the teaching quality of intervention teachers (relative to control group teachers) were sustained. Results indicated sustained high-quality implementation of some curriculum components (the Promoting Alternative THinking Strategies curriculum) but decreased implementation of other components (the language/literacy components). Sustained intervention effects were evident on most aspects of general teaching quality targeted by the intervention. Practice or Policy: Implications for practice and policy are discussed.