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

Cluster Sampling Method01:20

Cluster Sampling Method

12.0K
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...
12.0K
Calculating and Interpreting the Linear Correlation Coefficient01:11

Calculating and Interpreting the Linear Correlation Coefficient

6.1K
The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable, x, and the dependent variable, y. Hence, it is also known as the Pearson product-moment correlation coefficient. It can be calculated using the following equation:
6.1K
Coefficient of Correlation01:12

Coefficient of Correlation

6.3K
The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the...
6.3K
Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

3.0K
When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
3.0K
Calibration Curves: Correlation Coefficient01:10

Calibration Curves: Correlation Coefficient

1.7K
In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the...
1.7K
Sampling Plans01:23

Sampling Plans

221
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...
221

You might also read

Related Articles

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

Sort by
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

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

Statistics in medicine·2026
Same author

Doubly Robust Estimators of the Restricted Mean Time in Favor Estimands in Individual- and Cluster-Randomized Trials.

Statistics in medicine·2026
Same author

Bayesian Inference for Cluster-Randomized Trials With Multivariate Outcomes Subject to Both Truncation by Death and Missingness.

Statistics in medicine·2026
Same journal

Age at menarche and adverse pregnancy and perinatal outcomes: triangulating evidence from multivariable and Mendelian randomization analyses.

International journal of epidemiology·2026
Same journal

Life-course trajectories of cardiovascular disease risk factors in rural India: Andhra Pradesh Children and Parents Study (APCAPS) 2003-2023.

International journal of epidemiology·2026
Same journal

Cohort Profile Update: The Young Lives study.

International journal of epidemiology·2026
Same journal

From the departing Editors in Chief.

International journal of epidemiology·2026
Same journal

Data Resource Profile: Cheeloo Lifespan Electronic-health reseArch Data-library (Cheeloo LEAD).

International journal of epidemiology·2026
Same journal

Cohort Profile Update: The Swiss Childhood Cancer Survivor Cohort.

International journal of epidemiology·2026
See all related articles

Related Experiment Video

Updated: Jul 30, 2025

The Innovation Arena: A Method for Comparing Innovative Problem-Solving Across Groups
14:14

The Innovation Arena: A Method for Comparing Innovative Problem-Solving Across Groups

Published on: May 13, 2022

5.9K

Estimating intra-cluster correlation coefficients for planning longitudinal cluster randomized trials: a tutorial.

Yongdong Ouyang1,2, Karla Hemming3, Fan Li4,5

  • 1Clinical Epidemiology Program, Ottawa Hospital Research Institute, Ottawa, ON, Canada.

International Journal of Epidemiology
|May 17, 2023
PubMed
Summary
This summary is machine-generated.

Estimating correlation parameters for longitudinal cluster randomized trials (CRTs) is crucial for sample size calculations. This tutorial provides methods and code to estimate these parameters for various correlation structures, aiding future CRT design.

Keywords:
Sample sizeclinical trialscluster autocorrelation coefficientstatistical powerstepped wedge

More Related Videos

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
06:52

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

Published on: September 17, 2019

6.4K
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.4K

Related Experiment Videos

Last Updated: Jul 30, 2025

The Innovation Arena: A Method for Comparing Innovative Problem-Solving Across Groups
14:14

The Innovation Arena: A Method for Comparing Innovative Problem-Solving Across Groups

Published on: May 13, 2022

5.9K
Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
06:52

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

Published on: September 17, 2019

6.4K
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.4K

Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Epidemiology

Background:

  • Designing longitudinal cluster randomized trials (CRTs) necessitates estimating complex correlation structures beyond the basic intra-cluster correlation coefficient (ICC).
  • Accurate estimation of within-period ICC, cluster autocorrelation, and intra-individual autocorrelation is vital for sample size determination in advanced CRT designs.
  • Lack of readily available estimates from prior studies presents a significant challenge for investigators planning longitudinal CRTs.

Purpose of the Study:

  • To provide a tutorial on estimating correlation parameters for longitudinal CRTs.
  • To demonstrate methods for estimating parameters under exchangeable, nested/block exchangeable, and exponential decay correlation structures.
  • To offer practical guidance and programming code for continuous and binary outcomes.

Main Methods:

  • Introduction of correlation structures and their mixed-effects regression model assumptions.
  • Demonstration of parameter estimation techniques using practical examples.
  • Provision of programming code in R, SAS, and Stata, alongside an Rshiny app for data analysis.

Main Results:

  • The tutorial successfully demonstrates the estimation of correlation parameters for continuous and binary outcomes under specified correlation structures.
  • Practical implementation advice and reproducible code are provided for key statistical software.
  • An accessible Rshiny application is available to assist investigators in estimating these crucial parameters.

Conclusions:

  • Estimating correlation parameters is feasible using existing datasets or observational data.
  • The provided methods and tools facilitate more accurate sample size calculations for longitudinal CRTs.
  • Further research is needed to address identified gaps in the literature regarding correlation parameter estimation.