How Many Cases per Cluster - Operationalizing the Number of Units per Cluster Relative to Minimum Detectable Effects in Two-Level Cluster Randomized Evaluations with Linear Outcomes

Oct 15, 2026

Uploaded by Mabel

Cluster randomized evaluations assign an intervention to a set of clusters, each containing individual observational units; a key planning question is how many units per cluster are needed to achieve adequate statistical power. The article challenges the common “about 30 units per cluster” rule by linking the ratio of the minimum detectable effect size to a related effect size using one fewer unit. It provides formulas for a subsequent difference effect size ratio (SDESR) and for deriving the required unit count under an assumed SDESR. Diminishing returns emerge earlier when intraclass correlation is larger.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages16

Reading Time40 min

AccessFree to download

Abstract

Keywords

Introduction and Motivation

Why Consider Units per Cluster?

Statistical Power and MDES for Two-Level Cluster Randomized Evaluations

SDESR and Formulas for Unit Counts per Cluster

Implications, Examples, and Extensions with Covariates

How Many Cases per Cluster? Operationalizing the Number of Units per Cluster Relative to Minimum Detectable Effects in Two-Level Cluster Randomized Evaluations with Linear Outcomes E. C. Hedberg 1 American Journal of Evaluation 2023, Vol. 44(1) 153-168 © The Author(s) 2023 Article reuse guidelines: [sagepub.com/journals-permissions](sagepub.com/journals-permissions)[ ](sagepub.com/journals-permissions)[DOI: 10.1177/10982140221134618](DOI: 10.1177/10982140221134618)[ ](DOI: 10.1177/10982140221134618)[journals.sagepub.com/home/aje](journals.sagepub.com/home/aje) Abstract In cluster randomized evaluations, a treatment or intervention is randomly assigned to a set of clusters each with constituent individual units of observations (e.g., student units that attend schools, which are assigned to treatment). One consideration of these designs is how many units are needed per cluster to achieve adequate statistical power. Typically, researchers state that “about 30 units per cluster” is the most that will yield beneﬁt towards statistical precision. To avoid rules of thumb not grounded in statistical theory and practical considerations, and instead provide guidance for this question, the ratio of the minimum detectable effect size (MDES) to the larger MDES with one less unit per cluster is related to the key parameters of the cluster randomized design. Formulas for this subsequent difference effect size ratio (SDESR) at a given number of units are provided, as are formulas for ﬁnding the number of units for an assumed SDESR. In general, the point of diminishing returns occurs with smaller numbers of units for larger values of the intraclass correlation. Keywords statistical power, sample size, cluster randomized designs, experiments In cluster randomized evaluations, an intervention is randomly assigned to a subset of clusters, within which there are individual units of observations. For example, n student units each attend M schools, which are assigned to treatment or control, which together constitutes the total sample of nM = N. Within this design, researchers planning cluster randomized evaluations commonly: “how many units per cluster are needed for our evaluation design and assumptions?” This 1 Abt Associates, Rockville, MD, USA Corresponding Author: E. C. Hedberg, Abt Associates, 6130 Executive Blvd Rockville, MD 20852 USA. Email: [hedbergec@gmail.com](hedbergec@gmail.com) article alters this question to ask instead: at what number of units per cluster is adding an additional unit to each cluster no longer practically beneﬁcial? The latter question requires both an understanding of how each additional unit improves sensitivity to detect the effect of treatment and how we can measure a practical point at which the improvement in sensitivity is no longer substantively helpful to the evaluation. For a hypothetical example of the types of decisions in planning evaluations that this article can help rationalize, suppose an evaluation of a nursing home staff anxiety prevention program is being planned. Treatment is to be assigned by nursing home and the dependent variable, an anxiety scale, will be measured for each individual licensed practical nurse (LPN) . The number of nursing homes available to be randomized is ﬁxed. It is expected that about 30 percent 1 of the variation in the outcome occurs between nursing home, and a covariate is available that explains about 25 percent of the individual-level variation and 50 percent of the between cluster variation. Please note these values are entirely hypothetical. A concern is that each of the participating nursing homes have on average ten LPNs, but only about eight LPNs per nursing home are expected to participate in the study. Increasing the effort by evaluation team members and survey incentives to add a one nurse per home would add a considerable amount to the evaluation budget. Is this expenditure worth theresources? The results below allow for a compu

FAQs

为什么在集群随机评估中需要关注每个集群的单位数？

因为单位数会影响研究对处理效应的敏感度，从而影响统计功效与最小可检测效应。文章指出，这个问题不应只强调增加集群数量。

文章如何避免使用“每集群约30个单位”的经验性规则？

通过将最小可检测效应（MDES）与“每集群少一个单位”对应的更大MDES之间的比值联系到两层集群随机设计的关键参数，并据此给出推导公式。

SDESR与“何时增加单位不再有实质价值”有什么关系？

文章提出后续差异效应大小比率（SDESR），用来概括把每个集群再增加一个单位对MDES带来的实际收益；并进一步提供在给定SDESR假设下求取单位数n的公式。

Oct 15, 2026

Uploaded by Mabel