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Design effects for sample size computation in three-level designs.

Tina D Cunningham¹, Robert E Johnson²

¹Graduate Program in Public Health, Eastern Virginia Medical School, Norfolk, VA, USA CunninTD@evms.edu.

Statistical Methods in Medical Research

|October 17, 2012

Summary

This summary is machine-generated.

Calculating sample sizes for complex experiments is challenging. This study provides unified formulas for design effects and sample size computation in multi-level randomized studies, using intracluster correlations.

Keywords:

Sample size design effects three-level design

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Area of Science:

Statistics
Biostatistics
Experimental Design

Background:

Sample size calculations are crucial for the validity of experiments.
Multi-level randomized experiments present unique challenges for traditional sample size formulas.
Existing methods often require adjustments using design effects or multiplicative factors.

Purpose of the Study:

To develop a unified approach for calculating sample sizes in multi-level randomized experiments.
To present formulas for design effects based on intracluster correlations.
To provide methods for computing sample sizes at different hierarchical levels.

Main Methods:

Derivation of design effects in terms of intracluster correlations.
Development of adjusted sample size formulas for nested experimental designs.
Assumption of equal cluster sample sizes and homogeneous within-cluster variances.

Main Results:

A unified framework for understanding and calculating design effects in multi-level studies.
Formulas for sample size computation applicable to various levels of randomization.
Demonstration of how intracluster correlations influence sample size requirements.

Conclusions:

The proposed unified approach simplifies sample size calculations in complex experimental settings.
Intracluster correlations are key parameters for adjusting sample sizes in nested designs.
The formulas facilitate accurate sample size determination for multi-level randomized experiments.