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Related Concept Videos

Sample Size Calculation01:19

Sample Size Calculation

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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.
The sample size for the given experiment or sampling effort is fundamental to any study design. Sample size decides the number of...
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One-Way ANOVA: Equal Sample Sizes01:15

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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.
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One-Way ANOVA: Unequal Sample Sizes01:15

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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:
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Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

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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...
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Bioequivalence Experimental Study Designs: Repeated Measures, Cross-Over, Carry-Over, and Latin Square Designs01:15

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Body:Bioequivalence experimental study designs play a pivotal role in testing the effectiveness of various treatments. Key among these are the repeated measures, cross-over, carry-over, and Latin square designs. In the repeated measures design, each subject receives all treatments, allowing for temporal comparisons. This type of design is useful in reducing variability but requires careful planning to avoid bias.The cross-over design, an economical method, involves sequential administration of...
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Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

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Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures...
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Power and Sample Size for Fixed-Effects Inference in Reversible Linear Mixed Models.

Yueh-Yun Chi1, Deborah H Glueck2, Keith E Muller3

  • 1Department of Biostatistics, University of Florida.

The American Statistician
|February 12, 2020
PubMed
Summary
This summary is machine-generated.

Accurate power and sample size calculations for general linear mixed models are now available. These methods, applicable to longitudinal and clustered data, use multivariate test distributions and are accessible via free software.

Keywords:
Cluster designGeneral Linear Multivariate ModelLongitudinalMANOVAMultilevelRepeated measures

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Area of Science:

  • Statistics
  • Biostatistics
  • Longitudinal Data Analysis

Background:

  • General linear mixed models (GLMMs) are popular but lack accessible power and sample size calculation tools.
  • Current methods often rely on simulations or approximations, leading to misalignment with actual data analysis.

Purpose of the Study:

  • To provide accurate power and sample size approximations for inference in reversible linear models, including those with longitudinal and clustering features.
  • To demonstrate the equivalence of the GLMM Wald test to well-studied multivariate tests for power and sample size calculations.

Main Methods:

  • Utilizing the non-central distributions of the multivariate Hotelling-Lawley test to derive power and sample size results for the GLMM Wald test.
  • Developing easily computable methods using a free, open-source web-based product and offering approximations for missing data.

Main Results:

  • Established exact and approximate power and sample size results for the mixed-model Wald test, equivalent to multivariate test results.
  • Demonstrated the applicability of these methods through a real-world example of a multicenter study on pregnancy with clustered data.

Conclusions:

  • The developed methods offer accurate and accessible power and sample size calculations for GLMMs, addressing a significant gap in statistical software.
  • The findings facilitate robust study design for longitudinal and clustered data, enhancing the reliability of statistical inference.