Power Analyses for Moderator Effects in Three-Level Cluster Randomized Trials

Researchers are often interested in whether the effects of an intervention differ conditional on individual- or group-moderator variables such as children's characteristics (e.g., gender), teacher's background (e.g., years of teaching), and school's characteristics (e.g., urbanity); that is, the researchers seek to examine for whom and under what circumstances an intervention works. Furthermore, the researchers are interested in understanding and interpreting variability in treatment effects through moderation analysis as an approach to exploring the sources of the treatment effect variability. This study develops formulas for power analyses to detect the moderator effects in designing three-level cluster randomized trials (CRTs). We develop the statistical formulas for calculating statistical power, minimum detectable effect size difference, and 95% confidence intervals for cluster or cross-level moderation, nonrandomly varying or random slopes, binary or continuous moderators, and designs with or without covariates. We demonstrate how the calculations can be used in the planning phase of three-level CRTs using the software PowerUp!-Moderator.     

The Power of the Test for Treatment Effects in Three-Level Cluster Randomized Designs

Abstract

Experiments that involve nested structures often assign entire groups (such as schools) to treatment conditions. Key aspects of the design of such experiments include knowledge of the intraclass correlation structure and the sample sizes necessary to achieve adequate power to detect the treatment effect. This study provides methods for computing power in three-level cluster randomized balanced designs (with two levels of nesting), where, for example, students are nested within classrooms and classrooms are nested within schools and schools are assigned to treatments. The power computations take into account nesting effects at the second (classroom) and at the third (school) level, sample size effects (e.g., number of schools, classrooms, and individuals), and covariate effects (e.g., pretreatment measures). The methods are applicable to quasi-experimental studies that examine group differences in an outcome.     

From Planning to Implementation: An Examination of Changes in the Research Design,Sample Size,and Precision of Group Randomized Trials Launched by the Institute of Education Sciences

Abstract

This article examines changes in the research design, sample size, and precision between the planning phase and implementation phase of group randomized trials (GRTs) funded by the Institute of Education Sciences. Thirty-eight GRTs funded between 2002 and 2006 were examined. Three studies revealed changes in the experimental design. Ten studies showed decreases in the total number of groups randomized, whereas 18 studies showed increases. In five cases, the decreases in the number of groups randomized were large enough to decrease the precision of the study. However, in the majority of the studies, the precision was relatively unchanged from planning phase to implementation phase. The consistency in the precision between the planning phase and implementation phase highlights the importance of planning adequately powered studies.     

The Power of the Test for Treatment Effects in Three-Level Block Randomized Designs

Abstract

Experiments that involve nested structures may assign treatment conditions either to subgroups (such as classrooms) or individuals within subgroups (such as students). The design of such experiments requires knowledge of the intraclass correlation structure to compute the sample sizes necessary to achieve adequate power to detect the treatment effect. This study provides methods for computing power in three-level block randomized balanced designs (with two levels of nesting) where, for example, students are nested within classrooms and classrooms are nested within schools. The power computations take into account nesting effects at the second (classroom) and at the third (school) level, sample size effects (e.g., number of level-1, level-2, and level-3 units), and covariate effects (e.g., pretreatment measures). The methods are generalizable to quasi-experimental studies that examine group differences on an outcome.     

Assessing the Precision of Multisite Trials for Estimating the Parameters of a Cross-Site Population Distribution of Program Effects

Multisite trials, which are being used with increasing frequency in education and evaluation research, provide an exciting opportunity for learning about how the effects of interventions or programs are distributed across sites. In particular, these studies can produce rigorous estimates of a cross-site mean effect of program assignment (intent-to-treat), a cross-site standard deviation of the effects of program assignment, and a difference between the cross-site mean effects of program assignment for two subpopulations of sites. However, to capitalize on this opportunity will require adequately powering future trials to estimate these parameters. To help researchers do so, we present a simple approach for computing the minimum detectable values of these parameters for different sample designs. The article then uses this approach to illustrate for each parameter, the precision trade-off between increasing the number of study sites and increasing site sample size. Findings are presented for multisite trials that randomize individual sample members and for multisite trials that randomize intact groups or clusters of sample members.     

Progress in the past decade: an examination of the precision of cluster randomized trials funded by the U.S. Institute of Education Sciences

ABSTRACT

This article examines the statistical precision of cluster randomized trials (CRTs) funded by the Institute of Education Sciences (IES). Specifically, it compares the total number of clusters randomized and the minimum detectable effect size (MDES) of two sets of studies, those funded in the early years of IES (2002–2004) and those funded in the recent years (2011–2013). Overall, the average precision in terms of MDES of studies in the recent cohort was more than double that of the early cohort (i.e. 0.48 compared to 0.23). The findings suggest a consistent and substantial increase in the precision of CRTs funded by IES in the past decade which is a critical step towards designing studies that have the potential to yield high-quality evidence about the effectiveness of educational interventions.     

Effects of a Pre-Kindergarten Mathematics Intervention: A Randomized Experiment

Abstract

Research indicates that a socioeconomic status-related gap in mathematical knowledge appears early and widens during early childhood. Young children from economically disadvantaged families receive less support for mathematical development both at home and in preschool. Consequently, children from different socioeconomic backgrounds enter elementary school at different levels of readiness to learn a standards-based mathematics curriculum. One approach to closing this gap is the development and implementation of effective mathematics curricula for public preschool programs enrolling economically disadvantaged children. A randomized controlled trial was conducted in 40 Head Start and state preschool classrooms, with 278 children, to determine whether a pre-kindergarten mathematics intervention was effective. Intervention teachers received training that enabled them to implement with fidelity, and a large majority of parents regularly used math activities teachers sent home. Intervention and control groups did not differ on math assessments at pretest; however, gain scores of intervention children were significantly greater than those of control children at posttest. Thus, the intervention reduced the gap in children's early mathematical knowledge.     

New Empirical Evidence for the Design of Group Randomized Trials in Education

Abstract

This article provides practical guidance for researchers who are designing studies that randomize groups to measure the impacts of educational interventions. The article (a) provides new empirical information about the values of parameters that influence the precision of impact estimates (intraclass correlations and R ² values) and includes outcomes other than standardized test scores and data with a three-level structure rather than a two-level structure, and (b) discusses the error (both generalizability and estimation error) that exists in estimates of key design parameters and the implications this error has for design decisions. Data for the paper come primarily from two studies: the Chicago Literacy Initiative: Making Better Early Readers Study (CLIMBERS) and the School Breakfast Pilot Project (SBPP). The analysis sample from CLIMBERS comprised 430 four-year-old children from 47 preschool classrooms in 23 Chicago public schools. The analysis sample from the SBPP study comprised 1,151 third graders from 233 classrooms in 111 schools from 6 school districts. Student achievement data from the Reading First Impact Study is also used to supplement the discussion.     

A Test for Cluster Bias: Detecting Violations of Measurement Invariance Across Clusters in Multilevel Data

We present a test for cluster bias, which can be used to detect violations of measurement invariance across clusters in 2-level data. We show how measurement invariance assumptions across clusters imply measurement invariance across levels in a 2-level factor model. Cluster bias is investigated by testing whether the within-level factor loadings are equal to the between-level factor loadings, and whether the between-level residual variances are zero. The test is illustrated with an example from school research. In a simulation study, we show that the cluster bias test has sufficient power, and the proportions of false positives are close to the chosen levels of significance.     

企业群内企业规模难以扩张的经济学分析

企业群内企业规模普遍比较小,且难以扩张,造成这种现象的原因主要有:一是群内企业间存在交易成本节约机制;二是随着企业规模扩张,群内企业尤其是规模相对较大的企业组织成本呈现边际加速增长趋势。群内企业要实现规模有效扩张,前提就在于节约组织成本。     

基于层次分析法和聚类分析法的高等教育自学考试多元评价模型探析

在高等教育自学考试中采用多元评价方式,有利于对学生进行全面评价,符合新时代教育评价改革要求。基于层次分析法和聚类分析法构建自学考试课程多元评价模型,以普通高等学校计算机基础课程为例进行实证分析,确定多元评价模型各评价指标的权重系数,其中:终结性考试权重为0.539,实践成绩类权重为0.297,平时成绩类权重为0.164。该模型既体现了指标数据的客观性,又体现了考核主体的主观意志。     

近二十年我国基础教育改革热点的聚类分析——学术与政策的文本考查

为把握基础教育改革方向,明晰基础教育的未来议题,夯实教育现代化进程的奠基工程,以2000年至2020年间的学术和政策两类文本为样本,探寻该领域的改革热点。学术文本以CSSCI中基础教育类的四本期刊中782篇论文为代表,政策文本以教育部以上部门出台的173份政策为代表,以SATI3.2和SPSS22.0为工具,进行     

Pre-service Mathematics Teaching in the Context of Schools: An Exploration into the Constitution of Identity

This paper engages withpoststructural ideas for a discussion on whatit means to engage in pedagogical work in thecontext of elementary/primary schoolmathematics classrooms. Central to the analysisare the pre-service student and the part thatthe teaching practicum plays in the `making' ofa teacher. Drawing on insights from the work ofFoucault on power and subjectivity, instancesof teaching knowledge in production, asinterpreted by pre-service teachers, areexamined. The view is towards developing theoryfrom readings of specific regulatory strategiesthat impact powerfully on pre-service teachers'constructions of themselves as mathematicsteachers.     

高校英语教学中运用文化导入的教学效果分析

以浙江林学院2002级学生为对象,将学生分成实验班和对照班,通过两个学年的教学,(实验班运用文化导入教学,对照班采用普通教学),运用相关分析和T检验的方法,对两个班的语言能力和社会文化能力进行测试和分析,结果表明实验班教学效果显著,因此高校英语教学中运用文化导入教学对提高学生跨文化交际能力具有积极的意义。     

论传统文化的消极因素对执政党建设的不良影响

中国传统文化中的优秀精华对我们今天加强党的建设,提高执政能力是有很好的促进作用,但其中的封建专制思想、官本位意识、官僚主义、宗法观念等消极因素以及其他封建没落思想,对当前执政党建设也产生着诸多不良影响。深入剖析这些腐朽思想存在的原因及其危害,可以做到鉴古知今,为加强党的思想作风建设、永葆党的先进性服务。     

中国大众传播媒介法制传播负效果分析

大众传播媒介在法制传播中担当着重要角色 ,但同时也产生了一些负面效果 ,主要是 :法制传播文本出现信息误差 ,从而误导受众 ;侵害民事主体的名誉权 ;色情、暴力内容充斥法制传播文本 ,误导受众 (尤其是青少年 )的价值观 ,引发犯罪 ;媒介监督职能行使不当 ,影响司法的独立与公正。     

1977年高考:一次空前的招生考试

1977年的高考,不仅是许多人命运的转折点,而且成为一个国家与时代的拐点。该年8月科教工作座谈会上一些专家提出恢复高考的建议,只是邓小平决意恢复高考的诱因。恢复高考最主要的因素是邓小平高瞻远瞩,力挽狂澜。1977年的高考是中国历史上最特别、最壮观的一次高考,也是是空前的。恢复高考意义重大而深远,中国的现代化征程,中国教育的复苏,当代中国的崛起,几乎都以恢复高考为出发的原点,由此中国社会历史掀开了崭新的一页。     

新课程高考改革方案：制度安排的预期与实际

以《普通高中课程标准》为教学背景的宁、鲁、琼、粤四省《新课程高考方案》已制订出台,作为制度安排,有其预设的期望,但实际效果将是各方博弈的结果。高考科目设置的改革,只是高考改革的一方面,高考改革的核心是高考内容改革。2007年四省区高考命题能够体现《普通高中课程标准》的精神及“能力立意”的思想至何种程度,还有待进一步探讨。     

An Examination of the Influence of Institutional Context on Student Persistence at 4-Year Colleges and Universities: A Multilevel Approach

Using constructs from Bean's (1990) [In: D. Hossler and J. P. Bean (Eds.), The strategic management of college enrollments. San Francisco:Jossey-Bass] student attrition model and the Berger and Milem (2000) [In: J. C. Smart (Ed.), Higher education: Handbook of theory and research (Vol. XV, pp. 268–338). New York: Agathon Press] college impact model, national survey data, and multilevel modeling techniques, this study examines the extent to which persistence is influenced by the institutional context. The analytic sample is limited to first-time, full-time, degree-seeking undergraduates attending 4-year colleges and universities nationwide. This study finds that selectivity, as measured by the average student academic ability at an institution, has a contextual effect on college student persistence that reflects a positive increment to the chance of persistence that accrues to a student beyond student-level predictors of persistence. Although the implications of the findings are mainly for theory and methods, policy implications are discussed.     

统考组题:高考模式创新的经济学分析

高考改革的大势是由传统的统一考试转向更为个性化的单独考试,但这种变革在给考生和高校带来一定好处的同时,也引起个人和社会负担成本的大幅增加,并影响到教育公平.从经济学角度分析高考表明,更加完全的统一考试,加上自由的个性化组题和统分相结合,即构成统考组题模式.在这种模式下,考生"各得其所",高校"各取所需",避开对统一分数的过度竞争,实现社会的最优配置.个人(考生)仅负担一个很小的不变成本,只要稍微提高一点社会成本(高校的录取费用等),就可大幅度增加个人和高校的效用.