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Cluster Sampling Method

Cluster Sampling Method

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...

Sampling Plans

Sampling Plans

Sampling is a crucial step in analytical chemistry, allowing researchers to collect representative data from a large population. Common sampling methods include random, judgmental, systematic, stratified, and cluster sampling.
Random sampling is a method where each member of the population has an equal chance of being selected for the sample. It involves selecting individuals randomly, often using random number generators or lottery-type methods. For example, when analyzing the properties of a...

One-Way ANOVA: Unequal Sample Sizes

One-Way ANOVA: Unequal Sample Sizes

One-way ANOVA can be performed on three or more samples of unequal sizes. However, calculations get complicated when sample sizes are not always the same. So, while performing ANOVA with unequal samples size, the following equation is used:

One-Way ANOVA: Equal Sample Sizes

One-Way ANOVA: Equal Sample Sizes

One-Way ANOVA can be performed on three or more samples with equal or unequal sample sizes. When one-way ANOVA is performed on two datasets with samples of equal sizes, it can be easily observed that the computed F statistic is highly sensitive to the sample mean.
Different sample means can result in different values for the variance estimate: variance between samples. This is because the variance between samples is calculated as the product of the sample size and the variance between the...

Sample Size Calculation

Sample Size Calculation

Knowledge of the sample size is the first requirement to conduct random sampling or an experiment. The sample size is the total number of units, observations, or groups (in some cases) used to get the data to estimate a population parameter. As the name suggests, the sample size is that of the sample drawn from the population and differs from the population size.
The sample size for the given experiment or sampling effort is fundamental to any study design. Sample size decides the number of...

Randomized Experiments

Randomized Experiments

The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
Simple randomization
Simple...

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Related Experiment Video

Updated: Jul 7, 2026

The Adjuvant Efficacy of Angong Niuhuang Pill in the Treatment of Viral Encephalitis: A Meta-Analysis of Randomized Controlled Trials

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Statistical power and sample size requirements for three level hierarchical cluster randomized trials.

Moonseong Heo¹, Andrew C Leon

¹Department of Psychiatry, Weill Medical College of Cornell University, White Plains, New York 10605, USA. moh2002@med.cornell.edu

|February 13, 2008

Summary

This study presents a power function and sample size formulas for three-level cluster randomized clinical trials (cluster-RCTs). These methods accurately estimate the power needed to detect intervention effects at the subject level in complex health studies.

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Area of Science:

Biostatistics
Clinical Trials Methodology
Health Services Research

Background:

Cluster randomized clinical trials (cluster-RCTs) involve hierarchical data structures, with interventions assigned to clusters, then professionals, and finally subjects.
Accurate sample size determination is crucial for the validity and power of cluster-RCTs, especially with three levels of data.

Purpose of the Study:

To derive a closed-form power function for three-level cluster-RCTs.
To develop precise formulae for sample size calculation to detect intervention effects at the subject level.
To provide guidance for the design of cluster-RCTs.

Main Methods:

Utilized a mixed-effects linear regression model for three-level data.
Developed a test statistic based on maximum likelihood estimates.
Derived a closed-form power function and sample size formulae.

Main Results:

The derived formulae provide accurate theoretical power estimates.
Simulation studies confirmed that theoretical power closely matches empirical power estimates.
The methods are applicable for detecting intervention effects at the subject level.

Conclusions:

The developed statistical methods offer reliable tools for sample size determination in three-level cluster-RCTs.
These findings support efficient and robust trial design in complex healthcare interventions.
Recommendations are provided for optimizing the design phase of cluster-RCTs.