Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

One-Way ANOVA: Unequal Sample Sizes01:15

One-Way ANOVA: Unequal Sample Sizes

6.0K
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:
6.0K
One-Way ANOVA: Equal Sample Sizes01:15

One-Way ANOVA: Equal Sample Sizes

3.5K
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...
3.5K
Cluster Sampling Method01:20

Cluster Sampling Method

13.1K
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...
13.1K
Sampling Plans01:23

Sampling Plans

317
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...
317
Sample Size Calculation01:19

Sample Size Calculation

4.2K
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...
4.2K
Factorial Design02:01

Factorial Design

13.3K
Factorial Analysis is an experimental design that applies Analysis of Variance (ANOVA) statistical procedures to examine a change in a dependent variable due to more than one independent variable, also known as factors. Changes in worker productivity can be reasoned, for example, to be influenced by salary and other conditions, such as skill level. One way to test this hypothesis is by categorizing salary into three levels (low, moderate, and high) and skills sets into two levels (entry level...
13.3K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Correlates and predictors of self-efficacy among dementia caregivers: D-CARE findings.

Alzheimer's & dementia : the journal of the Alzheimer's Association·2026
Same author

Principal stratification with U-statistics under principal ignorability.

Journal of the Royal Statistical Society. Series B, Statistical methodology·2026
Same author

A comparison of methods for designing hybrid type 2 cluster-randomized trials with continuous effectiveness and implementation endpoints.

Statistical methods in medical research·2026
Same author

Addressing Cluster-Level Treatment Effect Heterogeneity in Sample Size Determination for Hierarchical 2 × 2 Factorial Designs.

Biometrical journal. Biometrische Zeitschrift·2026
Same author

A longitudinal investigation of aggression and social skills in autistic youth.

Research in autism·2026
Same author

Time-Varying Treatment Effect Models in Stepped-Wedge Cluster-Randomized Trials With Multiple Interventions.

Statistics in medicine·2026

Related Experiment Video

Updated: Oct 8, 2025

Sampling Soils in a Heterogeneous Research Plot
07:11

Sampling Soils in a Heterogeneous Research Plot

Published on: January 7, 2019

35.0K

Sample size calculation in hierarchical factorial trials with unequal cluster sizes.

Zizhong Tian1, Denise Esserman1,2, Guangyu Tong1,2

  • 1Department of Biostatistics, Yale University School of Public Health, New Haven, Connecticut, USA.

Statistics in Medicine
|January 3, 2022
PubMed
Summary

This study provides sample size formulas for hierarchical trials, crucial for testing treatment effects and interactions in suicide prevention research. The methods account for cluster size variations, improving accuracy in trial design.

Keywords:
coefficient of variationcontrolled effectinteraction testlinear mixed modelmarginal effectpower analysis

More Related Videos

Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations
12:27

Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations

Published on: February 15, 2017

7.1K
Problem-Solving Before Instruction PS-I: A Protocol for Assessment and Intervention in Students with Different Abilities
10:26

Problem-Solving Before Instruction PS-I: A Protocol for Assessment and Intervention in Students with Different Abilities

Published on: September 11, 2021

4.1K

Related Experiment Videos

Last Updated: Oct 8, 2025

Sampling Soils in a Heterogeneous Research Plot
07:11

Sampling Soils in a Heterogeneous Research Plot

Published on: January 7, 2019

35.0K
Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations
12:27

Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations

Published on: February 15, 2017

7.1K
Problem-Solving Before Instruction PS-I: A Protocol for Assessment and Intervention in Students with Different Abilities
10:26

Problem-Solving Before Instruction PS-I: A Protocol for Assessment and Intervention in Students with Different Abilities

Published on: September 11, 2021

4.1K

Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Public Health Research

Background:

  • Suicide prevention trials often involve complex hierarchical treatment allocation (cluster and individual levels).
  • Accurate sample size calculation is essential for reliably testing treatment effects and interactions in such designs.
  • Existing methods may not adequately address the nuances of hierarchical structures and varying cluster sizes.

Purpose of the Study:

  • To derive and validate sample size formulas for testing controlled and marginal treatment effects, as well as their interaction, within a linear mixed model framework.
  • To account for unequal cluster sizes and their impact on sample size requirements.
  • To provide practical tools for designing hierarchical factorial trials, exemplified by a suicide prevention study.

Main Methods:

  • Development of sample size formulas based on z-approximation for large samples and t-approximation for finite samples.
  • Relaxation of the equal cluster size assumption, expressing formulas as functions of cluster size mean and coefficient of variation.
  • Extensive simulations to validate the accuracy and performance of the derived formulas.

Main Results:

  • Sample size formulas for controlled and marginal effects, and their interaction, are derived.
  • Cluster size variability significantly impacts sample size, particularly for cluster-level treatments.
  • The sample size for interaction effects is directly related to that of individual-level treatments.
  • Simulations confirm the accuracy of the formulas, with t-approximations offering better type I error control for small cluster numbers.

Conclusions:

  • The proposed sample size formulas provide a robust framework for designing hierarchical factorial trials.
  • The findings highlight the importance of considering cluster size variability in sample size calculations.
  • The developed methods, implemented in the R package H2x2Factorial, facilitate efficient trial design for interventions like suicide prevention programs.