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1.
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.  相似文献   

2.
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.  相似文献   

3.
An important concern when planning research studies is to obtain maximum precision of an estimate of a treatment effect given a budget constraint. When research designs have a multilevel or hierarchical structure changes in sample size at different levels of the design will impact precision differently. Furthermore, there will typically be differential costs of enrolling additional units at different levels of the hierarchy. The optimal design problem in multilevel research studies involves determining the optimal sample size at each level of the design given specified design parameters and a specified marginal cost of recruitment at each level. The current work extends existing results by considering optimal design for (a) unbalanced random assignment designs and (b) regression discontinuity designs.  相似文献   

4.
Abstract

This article develops a new approach for calculating appropriate sample sizes for school-based randomized control trials (RCTs) with binary outcomes using logit models with and without baseline covariates. The theoretical analysis develops sample size formulas for clustered designs where random assignment is at the school or teacher level using generalized estimating equation methods. The article focuses on the impact parameter pertaining to rates and proportions rather than to the log odds of response, which has been the focus of the previous literature. The article also compiles intraclass correlations (ICCs) for the clustered design for a range of binary outcomes using data from seven education RCTs. These ICCs and the power formulas are then used to conduct a power analysis using a provided SAS macro; the key finding is that sample sizes of 40 to 60 schools that are typically included in clustered RCTs for student test score or behavioral scale outcomes will often be insufficient for binary outcomes. A key reason is that the potential for precision gains from regression adjustment is likely to be smaller for binary outcomes.  相似文献   

5.
Abstract

Although the research methodology literature includes empirical benchmarks for effect sizes and intraclass correlations to help researchers determine adequate sample sizes through power analysis, it does not include similar benchmarks that would assist proper planning for attrition. To help fill this void, this paper describes how researchers can incorporate student attrition in power analyses and provides empirical benchmarks for the amount of attrition one might expect when conducting a school-based study that follows students over multiple years. The paper incorporates parameters for student attrition in common minimum detectable effect size calculations, presents attrition benchmarks based on student mobility rates in nationally representative longitudinal surveys, and presents benchmarks based on a synthesis of published evaluation studies. The paper includes a demonstration of how researchers can use the attrition benchmarks to take student attrition into account in a power analysis.  相似文献   

6.
ABSTRACT

Using a “naïve” specification, this paper estimates the relationship between 36 high school characteristics and 24 student outcomes controlling for students' pre-high school characteristics. The goal of this exploration is not to generate casual estimates, but rather to: (a) compare the size of the relationships to determine which inputs seem most promising and to identify which student outcomes appear most susceptible to being affected; (b) obtain likely upper-bound effect sizes that are useful information for power analyses used to establish minimum sample sizes for more robust designs capable of revealing causal impacts; and (c) illustrate how small effects over many outcomes (which are cumulatively important) can be easily missed. I find that most of the 36 inputs appear to have affected more outcomes than one would expect by chance, but that the apparent effects were generally small. Further, I find a higher frequency of large and significant apparent effects on educational achievement and attainment outcomes than labor market and other outcomes for young adults.  相似文献   

7.
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.  相似文献   

8.
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.  相似文献   

9.
Abstract

When well-implemented, mediation analyses play a critical role in probing theories of action because their results help lay the ground work for the critical development of a treatment and the iterative advancement of theories that are foundational to a discipline. Despite strong interest in designs that incorporate mediation, few studies have developed effective and efficient strategies to plan experiments examining multilevel mediation. We probe several design strategies for cluster-randomized designs and derive sampling plans that maximize power under cost constraints. The results suggest that among the more durable design strategies for mediation is covariance adjustment on variables predictive of the outcome and optimal sample allocation. The statistical power and optimal sample allocation results are implemented in the R package PowerUpR.  相似文献   

10.
Statistical power was estimated for 3 randomization tests used with multiple-baseline designs. In 1 test, participants were randomly assigned to baseline conditions; in the 2nd, intervention points were randomly assigned; and in the 3rd, the authors used both forms of random assignment. Power was studied for several series lengths (N = 10, 20, 30), several effect sizes (d = 0, 0.5, 1.0, 1.5, 2.0), and several levels of autocorrelation among the errors (p 1 = 0, .1, .2, .3, .4, and .5). Power was found to be similar among the 3 tests. Power was low for effect sizes of 0.5 and 1.0 but was often adequate (> .80) for effect sizes of 1.5 and 2.0.  相似文献   

11.
Abstract

Recent publications have drawn attention to the idea of utilizing prior information about the correlation structure to improve statistical power in cluster randomized experiments. Because power in cluster randomized designs is a function of many different parameters, it has been difficult for applied researchers to discern a simple rule explaining when prior correlation information will substantially improve power. This article provides bounds on the maximum possible improvement in power as a function of a single parameter, the number of clusters at the highest level of a multilevel experiment. The maximum improvement in power is less than 0.05 unless the number of clusters at the highest level is less than 20. Thus, the utility of using prior correlation information is limited to experiments with very small cluster-level sample sizes. Situations where small cluster-level sample sizes could still result in experiments with good statistical power are discussed, as is the relative utility of prior information about intracluster correlations as compared with covariate information that can explain cluster level variability in the outcome.  相似文献   

12.
Education experiments frequently assign students to treatment or control conditions within schools. Longitudinal components added in these studies (e.g., students followed over time) allow researchers to assess treatment effects in average rates of change (e.g., linear or quadratic). We provide methods for a priori power analysis in three-level polynomial change models for block-randomized designs. We discuss unconditional models and models with covariates at the second and third level. We illustrate how power is influenced by the number of measurement occasions, the sample sizes at the second and third levels, and the covariates at the second and third levels.  相似文献   

13.
The purpose of this study was to determine the proportion of empirical studies published in the last 5 years in a sample of special education peer‐reviewed journals that (1) assessed the effects of reading and math interventions with group designs and (2) used random assignment to treatment conditions to test those interventions. A hand search of articles from the Journal of Special Education, Exceptional Children, Learning Disabilities Research & Practice, the Journal of Learning Disabilities, and School Psychology Review yielded 806 relevant articles, of which 5.46 percent tested a reading or math intervention using a group design and 4.22 percent used random assignment. These findings indicate that randomized experimental designs, which offer the highest level of evidence of an intervention's efficacy, are underrepresented in the literature, at least in the area of reading and math interventions.  相似文献   

14.
Researchers are often interested in testing the effectiveness of an intervention on multiple outcomes, for multiple subgroups, at multiple points in time, or across multiple treatment groups. The resulting multiplicity of statistical hypothesis tests can lead to spurious findings of effects. Multiple testing procedures (MTPs) are statistical procedures that counteract this problem by adjusting p values for effect estimates upward. Although MTPs are increasingly used in impact evaluations in education and other areas, an important consequence of their use is a change in statistical power that can be substantial. Unfortunately, researchers frequently ignore the power implications of MTPs when designing studies. Consequently, in some cases, sample sizes may be too small, and studies may be underpowered to detect effects as small as a desired size. In other cases, sample sizes may be larger than needed, or studies may be powered to detect smaller effects than anticipated. This paper presents methods for estimating statistical power for multiple definitions of statistical power and presents empirical findings on how power is affected by the use of MTPs.  相似文献   

15.
The design of research studies utilizing binary multilevel models must necessarily incorporate knowledge of multiple factors, including estimation method, variance component size, or number of predictors, in addition to sample sizes. This Monte Carlo study examined the performance of random effect binary outcome multilevel models under varying methods of estimation, level-1 and level-2 sample size, outcome prevalence, variance component sizes, and number of predictors using SAS software. Mean estimates of statistical power were influenced primarily by sample sizes at both levels. In addition, confidence interval coverage and width and the likelihood of nonpositive definite random effect covariance matrices were impacted by variance component size and estimation method. The interactions of these and other factors with various model performance outcomes are explored.  相似文献   

16.
A computer program generated power functions of the Student t test and Mann-Whitney U test under violation of the parametric assumption of homogeneity of variance for equal and unequal sample sizes. In addition to depression and elevation of nominal significance levels of the t test observed by Hsu and by Scheffé, the entire power functions of both the t test and the U test were depressed or elevated. When the smaller sample was associated with a smaller variance, the U test was more powerful in detecting differences over the entire range of possible differences between population means. When sample sizes were equal, or when the smaller sample had the larger variance, the t test was more powerful over this entire range. These results show that replacement of the t test by a nonparametric alternative under violation of homogeneity of variance does not necessarily maximize correct decisions.  相似文献   

17.
Due to the clustered nature of field data, multi-level modeling has become commonly used to analyze data arising from educational field experiments. While recent methodological literature has focused on multi-level mediation analysis, relatively little attention has been devoted to mediation analysis when three levels (e.g., student, class, school) are present in a study setting. This article presents analysis models that can be used to test indirect effects in experimental designs having three levels where random assignment is at the third (school) or second (class) level and where the indirect effect may be random. In the presentation, simulated datasets are used to illustrate model specification and results interpretation for hypothetical three-level educational experiments involving mediation and moderation of treatment effects.  相似文献   

18.
ABSTRACT

Many educational policymakers consider attendance as a tool to induce learning. Researchers also agree that attendance has a positive effect on learning; however, there are few empirical studies that measure the nature and significance of that effect. The authors analyzed the effect of class attendance on academic performance and evaluated the existence and importance of a minimum attendance requirement. Using student data from a sample of public primary schools in Chile, and considering for endogeneity and sample selection bias, they found two important results. First, attendance had a relevant and statistically significant effect on educational performance. Second, the existence of a threshold was identified, but educational performance did not continue to decrease after a certain number of absences, which seems to contradict policies that have a minimum attendance requirement.  相似文献   

19.
A multi-objective optimization of non-uniform beams is presented for minimum radiated sound power and weight. The transfer matrix method is used to compute the structural and acoustic responses of a non-uniform beam accurately and efficiently. The multi-objective particle swarm optimization technique is applied to search the Pareto optimal solutions that represent various compromises between weight and sound radiation. Several constraints are imposed, which substantially reduce the volume fraction of feasible solutions in the design space. Two non-uniform beams with different boundary conditions are studied to demonstrate the multi-objective optimal designs of the structure.  相似文献   

20.
The study, using a Monte Carlo technique, was designed to investigate the effect of the differences in covariate means among the treatment groups on the significance level and the power of the F-test of the analysis of covariance. The results show that the covariate group means differences have little effect on the significance level if the covariate is highly correlated with the criterion variable. However, if the correlation is .4 or less, larger sample sizes are required. The effect on the power is more sensitive for smaller experiments. The larger the differences among covariate group means, the lower the actual power becomes compared to the approximate theoretical power.  相似文献   

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