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Related Concept Videos

One-Way ANOVA: Equal Sample Sizes01:15

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

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:
Two-Way ANOVA01:17

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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
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Multiple Regression

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Sign Test for Matched Pairs

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Sample Sizes Required to Detect Interactions between Two Binary Fixed-Effects in a Mixed-Effects Linear Regression

Andrew C Leon1, Moonseong Heo

  • 1Department of Psychiatry, Weill Medical College of Cornell University.

Computational Statistics & Data Analysis
|January 20, 2010
PubMed
Summary
This summary is machine-generated.

Sample size calculations for mixed-effects models are crucial for clinical trials. Detecting a two-way interaction requires four times the sample size needed for a main effect of similar magnitude.

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Area of Science:

  • Biostatistics
  • Clinical Trials Methodology
  • Longitudinal Data Analysis

Background:

  • Mixed-effects linear regression models are increasingly utilized for analyzing repeated measures in clinical trials.
  • Existing formulas primarily address sample size estimation for main effects and treatment-by-time interactions.
  • A gap exists in sample size estimation for interactions involving multiple factors in repeated measures designs.

Purpose of the Study:

  • To propose a formula for estimating the sample size needed to detect a two-way interaction in factorial designs with repeated continuous outcomes.
  • To validate the proposed formula through a simulation study assessing statistical power.

Main Methods:

  • Development of a sample size formula based on the variance of interactions being fourfold that of main effects.
  • Conducting a simulation study for mixed-effects linear regression models with random intercepts.
  • Varying parameters in the simulation: magnitude of effects (Δ), intraclass correlation (ρ), and number of repeated measures (k).

Main Results:

  • The simulation study confirmed that detecting a 2x2 interaction necessitates a sample size four times larger than that required for a main effect of equivalent magnitude.
  • Statistical power was evaluated across different effect sizes, intraclass correlations, and numbers of repeated measures.

Conclusions:

  • The proposed formula provides a method for sample size estimation for two-way interactions in repeated measures designs.
  • The findings underscore the substantial increase in sample size requirements for detecting interactions compared to main effects in these models.