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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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Stratified Sampling Method01:16

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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.
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Randomized Experiments01:13

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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
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Sampling Plans01:23

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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.
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Sample Size Calculation01:19

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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.
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Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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Related Experiment Video

Updated: Dec 29, 2025

Comparison of Predictive Performance of Three Lymph Node Staging Systems in Colorectal Signet Ring Cell Carcinoma Based on Machine Learning Model
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Sample size estimation for stratified individual and cluster randomized trials with binary outcomes.

Lee Kennedy-Shaffer1, Michael D Hughes1

  • 1Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, Massachusetts.

Statistics in Medicine
|February 1, 2020
PubMed
Summary
This summary is machine-generated.

Stratification can reduce sample size in randomized trials with binary outcomes, especially for large clusters or common events. However, for rare events or small clusters, the sample size benefits of stratification are minimal.

Keywords:
cluster randomized trialsdesign effectgeneralized estimating equationsintracluster correlation coefficientsample sizestratification

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Area of Science:

  • Biostatistics
  • Clinical Trials Methodology
  • Epidemiology

Background:

  • Individual randomized trials (IRTs) and cluster randomized trials (CRTs) with binary outcomes are common in research.
  • Logistic regression is frequently used for analysis, with generalized estimating equations for CRTs.
  • The impact of stratification on sample size for binary outcomes is less understood than for continuous outcomes.

Purpose of the Study:

  • To develop and present practical methods for estimating sample size in stratified IRTs and CRTs with binary outcomes.
  • To quantify the sample size reduction achieved by stratification compared to unstratified trials.
  • To illustrate these methods using a planned tuberculosis prevention CRT.

Main Methods:

  • Proposed easy-to-use sample size estimation methods for stratified IRTs and CRTs.
  • Calculated the ratio of sample sizes for stratified versus unstratified trials.
  • Considered scenarios with estimated or assumed within-stratum intracluster correlation coefficients (ICCs) for CRTs.

Main Results:

  • Stratification's impact on sample size varies significantly with event probability and cluster size.
  • For IRTs and CRTs with small clusters and low event probability, stratification offers minimal sample size reduction.
  • Practically important sample size reductions are achievable with stratification when event probability is not small or cluster sizes are large.

Conclusions:

  • New methods facilitate sample size estimation for stratified randomized trials with binary outcomes.
  • Stratification can lead to substantial sample size savings in specific scenarios, particularly in CRTs with large clusters or higher event rates.
  • Investigators can use these methods to assess the trade-offs of stratification during trial planning.