Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Estimating Population Mean with Unknown Standard Deviation

Estimating Population Mean with Unknown Standard Deviation

In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
William S. Gosset (1876–1937) of the Guinness...

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...

Estimating Population Mean with Known Standard Deviation

Estimating Population Mean with Known Standard Deviation

To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate + error bound)
The...

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:

Estimating Population Standard Deviation

Estimating Population Standard Deviation

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...

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...

You might also read

Related Articles

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

Sort by

Same author

Polypill for heart failure with reduced ejection fraction: the POLY-HF randomized trial.

Nature medicine·2026

Same author

Stress and cardiovascular disease: Testing a vigilance pathway in two contemporary theories.

Health psychology : official journal of the Division of Health Psychology, American Psychological Association·2026

Same author

Monoclonal antibodies targeting PCDH7 inhibit tumor growth and enhance immune responses in <i>KRAS</i>-mutant non-small cell lung cancer.

Science advances·2026

Same author

Involved nodal versus elective neck radiotherapy (INVERT) for head and neck squamous cell carcinoma: a prospective phase II randomized controlled trial protocol.

BMC cancer·2026

Same author

Sample Size Determination for Comparing Slopes in Cluster Randomized Trials With Longitudinal Measurements.

Statistics in medicine·2026

Same author

Undetected Weight Loss Associates With Upstaging in Cancer Patients.

Journal of cachexia, sarcopenia and muscle·2026

Search research articles

Related Experiment Video

Updated: May 22, 2026

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems

Published on: July 30, 2019

Sample size calculation for time-averaged differences in the presence of missing data.

Song Zhang¹, Chul Ahn

¹Department of Clinical Sciences, UT Southwestern Medical Center, 5323 Harry Hines Blvd, Dallas, TX 75390-9066, United States. Song.Zhang@utsouthwestern.edu

Contemporary Clinical Trials

|May 4, 2012

Summary

This summary is machine-generated.

This study introduces a new sample size formula for repeated measures studies with missing data. It extends previous work by using the generalized estimating equation (GEE) method for time-averaged differences.

More Related Videos

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

Measuring Delay Discounting in Humans Using an Adjusting Amount Task

Measuring Delay Discounting in Humans Using an Adjusting Amount Task

Published on: January 9, 2016

Related Experiment Videos

Last Updated: May 22, 2026

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems

Modeling the Size Spectrum for Macroinvertebrates and Fishes in Stream Ecosystems

Published on: July 30, 2019

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

Measuring Delay Discounting in Humans Using an Adjusting Amount Task

Measuring Delay Discounting in Humans Using an Adjusting Amount Task

Published on: January 9, 2016

Area of Science:

Biostatistics
Clinical Trials
Longitudinal Data Analysis

Background:

Sample size calculations are crucial for the validity of repeated measures studies.
Existing formulas often do not account for missing data or complex correlation structures.
Previous work by Diggle et al. (2002) focused on time-averaged differences without missing data.

Purpose of the Study:

To extend existing sample size formulas for time-averaged differences in repeated measures studies.
To incorporate the effects of missing data and various correlation structures.
To provide a practical tool for researchers designing longitudinal studies.

Main Methods:

Utilized the generalized estimating equation (GEE) method for comparing time-averaged differences.
Developed a closed-form formula for sample size and power calculations.
Conducted simulation studies to evaluate the formula's performance under various conditions, including small sample sizes and different correlation structures.

Main Results:

The proposed GEE-based sample size formula effectively accounts for missing data and diverse correlation structures.
Simulation results demonstrate the formula's robustness, even with small sample sizes.
The formula provides a reliable method for sample size determination in longitudinal studies with incomplete data.

Conclusions:

The developed sample size formula offers a significant advancement for designing repeated measures studies with missing data.
The GEE approach provides a flexible framework for analyzing time-averaged differences in longitudinal data.
This methodology is applicable to various research settings, including clinical trials.