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Related Concept Videos

Poisson Probability Distribution01:09

Poisson Probability Distribution

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A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
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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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Choosing Between z and t Distribution01:25

Choosing Between z and t Distribution

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The z and the Student t distribution estimate the population mean using the sample mean and standard deviation. However, to decide which distribution to use for a calculation, one needs to determine the sample size, the nature of the distribution, and whether the population standard deviation is known. If the population standard deviation is known and the population is normally distributed, or if the sample size is greater than 30, the z distribution is preferred. The Student t distribution is...
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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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Random Sampling Method01:09

Random Sampling Method

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Sampling is a technique to select a portion (or subset) of the larger population and study that portion (the sample) to gain information about the population. Data are the result of sampling from a population. The sampling method ensures 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. Among the various sampling methods used by...
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Sampling Distribution01:12

Sampling Distribution

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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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Exact sample size determination for a single Poisson random sample.

Susanna Gentile1, Valeria Sambucini1

  • 1Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy.

Biometrical Journal. Biometrische Zeitschrift
|May 9, 2023
PubMed
Summary

This study compares classical and Bayesian methods for determining sample sizes in single-arm trials with Poisson data. It introduces a conservative approach for sample size calculation, accounting for discrete data, and provides an R Shiny app for reproducibility.

Keywords:
Poisson dataanalysis and design prior distributionsexact sample size determinationfully Bayesian approachhybrid classical Bayesian approach

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Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Statistical Power Analysis

Background:

  • Classical power analysis is standard for clinical trial sample size determination.
  • Bayesian approaches offer flexibility and incorporate prior information in study planning.
  • Single-arm trials with Poisson data require specific sample size considerations.

Purpose of the Study:

  • To compare classical, hybrid Bayesian, and fully Bayesian methods for sample size determination in single-arm Poisson trials.
  • To propose a conservative sample size criterion addressing the non-monotonic power function with discrete data.
  • To develop a reproducible tool for sample size calculation.

Main Methods:

  • Comparison of frequentist and Bayesian exact methods for hypothesis testing.
  • Application of a conservative sample size criterion for discrete data.
  • Development of an R Shiny web application for sample size computation.

Main Results:

  • The study provides a comparative analysis of different power analysis approaches.
  • A conservative criterion is suggested for accurate sample size determination in Poisson trials.
  • The developed Shiny app facilitates easy and reproducible sample size calculations.

Conclusions:

  • Bayesian methods offer a flexible alternative to classical power analysis for sample size determination.
  • The proposed conservative criterion enhances accuracy for discrete Poisson data.
  • The R Shiny app promotes reproducible and user-friendly sample size calculations in clinical research.