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Related Concept Videos

Poisson Probability Distribution01:09

Poisson Probability Distribution

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...
Crossover Experiments01:16

Crossover Experiments

Crossover experiments, also called the repeated-measurements design, is a study design in which all experimental units are exposed to all treatments in different periods. Crossover experiments are generally used in psychology, the pharmaceutical industry, agriculture, and medicine.
Crossover designs are performed even with smaller sample sizes since the samples can act as their controls. These are better than simple randomized trials since patients are exposed to all the treatments.
Hardy-Weinberg Principle01:49

Hardy-Weinberg Principle

Diploid organisms have two alleles of each gene, one from each parent, in their somatic cells. Therefore, each individual contributes two alleles to the gene pool of the population. The gene pool of a population is the sum of every allele of all genes within that population and has some degree of variation. Genetic variation is typically expressed as a relative frequency, which is the percentage of the total population that has a given allele, genotype or phenotype.
Poisson's Ratio01:23

Poisson's Ratio

Poisson's ratio is a material property that indicates their stress response. It explains the connection between the elongation or compression a material undergoes in the direction of an applied force and the contraction or expansion it experiences perpendicular to that force. When a slender bar is loaded axially, it stretches in the direction of the force and contracts laterally. Poisson's ratio is the negative ratio of this lateral contraction to the axial elongation. The negative sign ensures...
Frequency-dependent Selection01:21

Frequency-dependent Selection

When the fitness of a trait is influenced by how common it is (i.e., its frequency) relative to different traits within a population, this is referred to as frequency-dependent selection. Frequency-dependent selection may occur between species or within a single species. This type of selection can either be positive—with more common phenotypes having higher fitness—or negative, with rarer phenotypes conferring increased fitness.
Parametric Survival Analysis: Weibull and Exponential Methods01:14

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
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Related Experiment Video

Updated: May 19, 2026

Frequency and Distribution of Crossovers in Caenorhabditis elegans Meiosis by SNP Genotyping using Real-time PCR
06:18

Frequency and Distribution of Crossovers in Caenorhabditis elegans Meiosis by SNP Genotyping using Real-time PCR

Published on: July 11, 2025

Analysis of Poisson frequency data under a simple crossover trial.

Kung-Jong Lui1, Kuang-Chao Chang2

  • 1Department of Mathematics and Statistics, College of Sciences, San Diego State University, San Diego, CA, USA kjl@rohan.sdsu.edu.

Statistical Methods in Medical Research
|August 18, 2012
PubMed
Summary

This study introduces new statistical methods for analyzing event frequencies in crossover trials. Asymptotic methods offer better power and precision for larger groups, while exact methods are useful for smaller sample sizes in Poisson distribution analyses.

Keywords:
Poisson distributioncount datacrossover designequalityequivalenceinterval estimatorsnon-inferioritypowerprecision

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Area of Science:

  • Biostatistics
  • Clinical Trial Design
  • Statistical Inference

Background:

  • Poisson distribution is frequently used to model event frequencies in clinical studies.
  • Crossover designs are efficient for comparing treatments, especially for chronic conditions.
  • Accurate statistical inference for treatment comparisons in crossover trials is crucial.

Purpose of the Study:

  • To develop and evaluate asymptotic and exact statistical procedures for analyzing the ratio of mean frequencies in a simple crossover design.
  • To provide methods for testing non-equality, non-inferiority, and equivalence of treatment effects.
  • To develop interval estimators for the ratio of mean frequencies.

Main Methods:

  • Development of asymptotic and exact test procedures for the ratio of mean frequencies.
  • Development of asymptotic and exact interval estimators for the ratio of mean frequencies.
  • Evaluation of performance using Monte Carlo simulations, assessing Type I error, power, and coverage probability.

Main Results:

  • Asymptotic test procedures demonstrate good Type I error control and superior power compared to exact tests for moderate to large sample sizes.
  • Asymptotic interval estimators with logarithmic transformation show improved precision over exact estimators without compromising coverage probability.
  • Exact test procedures and interval estimators are recommended for small sample sizes.

Conclusions:

  • Asymptotic methods provide efficient and accurate statistical inference for Poisson distributed event frequencies in crossover trials with sufficient sample size.
  • Exact methods remain valuable for situations with limited patient numbers per group.
  • The developed methods were illustrated using a randomized trial comparing salmeterol to placebo for asthma exacerbations.