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Related Concept Videos

Cluster Sampling Method01:20

Cluster Sampling Method

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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...
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Sample Size Calculation01:19

Sample Size Calculation

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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...
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One-Way ANOVA: Equal Sample Sizes01:15

One-Way ANOVA: Equal Sample Sizes

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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...
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One-Way ANOVA: Unequal Sample Sizes01:15

One-Way ANOVA: Unequal Sample Sizes

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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:
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Cell Size01:22

Cell Size

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Cell sizes vary widely among and within organisms. Bacterial cells range between 1-10 micrometers (μm)and are considerably smaller than most eukaryotic cells. The smallest bacteria are 0.1 μm in diameter—about a thousand times smaller than eukaryotic cells, which typically range from 10-100 μm.
Surface Area
Cells can take in nutrients and water via diffusion through the plasma membrane itself or through specific channels in the membrane. The area of the membrane surrounding...
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Stratified Sampling Method01:16

Stratified Sampling Method

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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. The sampling method ensures 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 stratified sample, divide the population into groups called strata and then take a...
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Related Experiment Video

Updated: Jan 25, 2026

A Simple Method for the Size Controlled Synthesis of Stable Oligomeric Clusters of Gold Nanoparticles under Ambient Conditions
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Sample size considerations for stratified cluster randomization design with binary outcomes and varying cluster size.

Xiaohan Xu1,2, Hong Zhu1, Chul Ahn1

  • 1Division of Biostatistics, Department of Clinical Sciences, University of Texas Southwestern Medical Center, Dallas, Texas.

Statistics in Medicine
|April 30, 2019
PubMed
Summary

This study introduces new sample size formulas for stratified cluster randomization trials (CRTs) that account for varying cluster sizes. These methods improve accuracy in estimating required participants and clusters, preventing underpowered or overpowered trials.

Keywords:
binary outcomescluster randomization designsample sizestratificationvarying cluster size

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Area of Science:

  • Clinical Trials Methodology
  • Biostatistics
  • Health Services Research

Background:

  • Stratified cluster randomization trials (CRTs) are widely used in health research to minimize baseline factor imbalance.
  • Existing sample size methods for CRTs often assume equal cluster sizes, which is unrealistic.
  • Varying cluster sizes can lead to inaccurate sample size estimations and impact trial power.

Purpose of the Study:

  • To develop accurate sample size formulas for stratified CRTs with binary outcomes, considering both clustering and varying cluster sizes.
  • To provide methods for estimating the total number of subjects and the number of clusters per group per stratum.
  • To assess the impact of varying cluster sizes on sample size calculations in stratified CRTs.

Main Methods:

  • Development of closed-form sample size formulas based on the Cochran-Mantel-Haenszel statistic.
  • Accounting for both cluster effect and variability in cluster sizes.
  • Simulation studies to evaluate the performance of the proposed sample size method.

Main Results:

  • Proposed formulas provide accurate estimations for sample size in stratified CRTs with unequal cluster sizes.
  • Varying cluster sizes significantly impact the required number of clusters, necessitating adjusted calculations.
  • The method demonstrates good finite-sample performance in simulations.

Conclusions:

  • The developed sample size formulas offer a more precise approach for designing stratified CRTs with varying cluster sizes.
  • Accurate sample size estimation is crucial for ensuring adequate power and reliable results in clinical trials.
  • The findings are applicable to various health research settings, including chronic disease management studies.