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Related Concept Videos

Pore Size Distribution01:23

Pore Size Distribution

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In concrete, the pore size distribution significantly influences the material's properties. Capillary pores, markedly larger than gel pores, form a vast network within partially hydrated cement paste, reducing the concrete's strength and increasing its permeability. This heightened permeability leads to a greater risk of damage from environmental factors like freeze-thaw cycles and chemical attacks, with the extent of vulnerability also being tied to the water-to-cement ratio.
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Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
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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.
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Cell sizes vary widely among and within organisms. Bacterial cells range between 1-10 micrometers (μm)and are considerably smaller than most eukaryotic cells. The smallest bacteria are 0.1 μm in diameter—about a thousand times smaller than eukaryotic cells, which typically range from 10-100 μm.
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Analysis and Specification of Starch Granule Size Distributions
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A noniterative sample size procedure for tests based on t distributions.

Yongqiang Tang1

  • 1Shire, 300 Shire Way, Lexington, MA, 02421, U.S.A.

Statistics in Medicine
|June 8, 2018
PubMed
Summary
This summary is machine-generated.

A new noniterative sample size method is proposed for t-distribution hypothesis tests, enhancing accuracy for clinical trials using ANCOVA and mixed models. This approach provides precise estimates, especially for smaller sample sizes.

Keywords:
Kenword-Roger varianceanalysis of covariancecrossover trialequivalence and bioequivalence trialsexact powermixed effects models for repeated measuresnoninferiority trial

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Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Statistical Inference

Background:

  • Accurate sample size determination is crucial for the validity and efficiency of clinical trials.
  • Existing methods for sample size calculation, particularly those involving t-distribution-based tests, may lack precision or require iterative computations.
  • Analysis of Covariance (ANCOVA) and mixed-effects models for repeated measures are commonly used in clinical trials but require appropriate sample size considerations.

Purpose of the Study:

  • To propose a noniterative sample size procedure for general hypothesis tests based on the t distribution.
  • To extend Guenther's approach for one- and two-sample t-tests to more complex scenarios like ANCOVA and mixed-effects models.
  • To provide accurate sample size and power calculations for various trial designs, including superiority, noninferiority, and equivalence tests.

Main Methods:

  • A generalized noniterative sample size procedure is developed by modifying and extending Guenther's method.
  • Correction terms are added to normal approximation sample sizes to account for t-statistic nonnormality and variance terms dependent on covariates.
  • Accurate power formulae for ANCOVA and mixed-effects models for repeated measures are derived, with the ANCOVA formula being exact for normally distributed covariates.

Main Results:

  • The proposed noniterative procedure yields exact or nearly exact sample size estimates, suitable for superiority, noninferiority, and equivalence tests.
  • The method accurately determines sample sizes without requiring specification of the covariate distribution.
  • Numerical examples confirm the accuracy of the proposed methods, particularly demonstrating their effectiveness in small sample scenarios.

Conclusions:

  • The developed noniterative sample size procedure offers a practical and accurate tool for clinical trial design involving t-distribution-based tests.
  • The method effectively handles complex statistical models like ANCOVA and mixed-effects models for repeated measures.
  • This approach enhances the precision of sample size and power calculations, especially beneficial for studies with limited sample sizes.