Linda Reichwein Zientek

Tools to Support Interpreting Multiple Regression in the Face of Multicollinearity

While multicollinearity may increase the difficulty of interpreting multiple regression (MR) results, it should not cause undue problems for the knowledgeable researcher. In the current paper, we argue that rather than using one technique to investigate regression results, researchers should consider multiple indices to understand the contributions that predictors make not only to a regression model, but to each other as well. Some of the techniques to interpret MR effects include, but are not limited to, correlation coefficients, beta weights, structure coefficients, all possible subsets regression, commonality coefficients, dominance weights, and relative importance weights. This article will review a set of techniques to interpret MR effects, identify the elements of the data on which the methods focus, and identify statistical software to support such analyses.

Preparing High-Quality Teachers: Views From the Classroom:

Every child has the right to a highly qualified teacher, yet as a nation we are reluctant to empirically investigate how teacher preparation programs are succeeding. Results from the present study suggested that (a) traditionally certified (TC) teachers felt better prepared than non–traditionally certified (NTC) teachers on communicating, planning, and using instructional strategies; (b) NTC teachers’ positive mentoring and prior classroom experiences in conjunction with the overall less positive mentoring experiences of TC teachers may have minimized differences; (c) novice teachers did not feel prepared on items related to multicultural curriculum or assessing student learning; and (d) prior classroom experiences, first year support, and program components were important, but instruction on teaching standards was of particular importance for NTC teachers.

Commonality Analysis: Partitioning Variance to Facilitate Better Understanding of Data

In early intervention, researchers often are interested in interpretation aids that can help determine the relative importance of variables when multiple regression models are used, and that facilitate deeper insight into prediction dynamics. Commonality analysis is one approach for helping researchers understand the contributions independent or predictor variables make in a given regression model. The purposes of the present paper are to (a) provide a general overview of multiple regression analysis and its application in early intervention research, (b) explain how to conduct a commonality analysis, and (c) illustrate how commonality analysis might be used as an interpretation aid in an early intervention research context.

Matrix Summaries Improve Research Reports: Secondary Analyses Using Published Literature

Correlation matrices and standard deviations are the building blocks of many of the commonly conducted analyses in published research, and AERA and APA reporting standards recommend their inclusion when reporting research results. The authors argue that the inclusion of correlation/covariance matrices, standard deviations, and means can enhance findings in education and psychology by permitting secondary researchers to (a) conduct commonly utilized traditional univariate and multivariate analyses not initially performed in primary studies, (b) produce effect sizes and other statistics not included in prior published literature, and (c) conduct analyses once difficult to perform. Furthermore, meta-analytic thinking is encouraged when researchers have the ability to conduct the same analyses on multiple studies and then compare these findings across studies.

Reporting Practices in Quantitative Teacher Education Research: One Look at the Evidence Cited in the AERA Panel Report

The authors of this article examine the analytic and reporting features of research articles cited in Studying Teacher Education: The Report of the AERA Panel on Research and Teacher Education (Cochran-Smith & Zeichner, 2005b) that used quantitative reporting practices. Their purpose was to help to identify reporting practices that can be improved to further the creation of the best possible evidence base for teacher education. Their findings indicate that many study reports lack (a) effect sizes, (b) confidence intervals, and (c) reliability and validity coefficients. One possible solution is for journal editors to emphasize clearly the expectations established in Standards for Reporting on Empirical Social Science Research in AERA Publications (AERA, 2006).

Applying the bootstrap to the multivariate case: Bootstrap component/factor analysis

The bootstrap method, which empirically estimates the sampling distribution for either inferential or descriptive sstatistical purposes, can be applied to the multivariate case. When conducting bootstrap component, or factor, analysis, resampling results must be located in a common factor space before summary statistics for each estimated parameter can be computed. The present article describes a strategy for applying the bootstrap method to conduct either a bootstrap component or a factor analysis with a program syntax for SPSS. The Holzinger–Swineford data set is employed to make the discussion more concrete.

The assumption of a reliable instrument and other pitfalls to avoid when considering the reliability of data

The purpose of this article is to help researchers avoid common pitfalls associated with reliability including incorrectly assuming that (a) measurement error always attenuates observed score correlations, (b) different sources of measurement error originate from the same source, and (c) reliability is a function of instrumentation. To accomplish our purpose, we first describe what reliability is and why researchers should care about it with focus on its impact on effect sizes. Second, we review how reliability is assessed with comment on the consequences of cumulative measurement error. Third, we consider how researchers can use reliability generalization as a prescriptive method when designing their research studies to form hypotheses about whether or not reliability estimates will be acceptable given their sample and testing conditions. Finally, we discuss options that researchers may consider when faced with analyzing unreliable data.

Student Success in Developmental Mathematics Courses.

Mathematics is a particular stumbling block for community college students in developmental course work. The present study empirically investigated student-level and teacher-level factors that influence the success of community college students enrolled in developmental mathematics courses. Specifically, numerous variables in one statistical model were examined, which included student self-efficacy (SE) beliefs in various aspects of academic engagement, previous course difficulties, full-time teaching status, and class attendance policies. Multiple regression results show that attendance was the largest predictor for higher course grades, followed by repeating a mathematics course and students’ sense of SE. In the hierarchical line modeling (HLM) model, teachers’ full-time status was a significant predictor in the model, but when teaching status was controlled for, the remaining student belief variables in the model were not statistically significant except SE in Cognitive Strategies, Self-Regulated Learning, and Motivational Strategies. The results provide empirical support for increased communication between full- and part-time faculty members, implementation of attendance policies, academic interventions prior to students’ failures, and the need to address students’ sense of SE.

Characterizing the Mathematics Anxiety Literature Using Confidence Intervals as a Literature Review Mechanism.

ABSTRACT The authors report the contextualization of effect sizes within mathematics anxiety research, and more specifically within research using the Mathematics Anxiety Rating Scale (MARS) and the MARS for Adolescents (MARS-A). The effect sizes from 45 studies were characterized by graphing confidence intervals (CIs) across studies involving (a) adults not participating in studies focusing on remedial or entry-level mathematics students or teachers, (b) remedial mathematics and entry-level college mathematics students, (c) preservice and inservice teachers, and (d) 7–12th-grade students and rising college students. The results also illustrate how CIs can be useful in research syntheses, because CIs (a) encourage meta-analytic thinking, (b) provide information about the research precision of a literature, and (c) provide plausible estimates for parameter values even if initial research expectations are wildly wrong.

Differences of Mentoring Experiences across Grade Span among Principals, Mentors, and Mentees

The purpose of this mixed research study was to examine mentoring experiences specific to grade span through the perspective of principals, mentors, and mentees. An instrument containing items on demographics, administrative support, and mentoring program components was administered to first-year teachers (n = 998), mentors (n = 791), and principals (n = 73). Mentors’ attitudes towards mentoring were statistically significantly more positive than were the mentees’ attitudes, although, on average, the attitudes for both groups were positive. A statistically significant difference in attitudes emerged as a function of grade span, with elementary school mentees reporting the highest levels of motivation to be mentored and the greatest desire to observe veteran teachers. Qualitative analyses revealed that mentoring includes specific format, better matches, increased time for mentoring, observation opportunities, and better training for mentors. Implications are discussed.