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Related Concept Videos

Introduction to Test of Independence01:21

Introduction to Test of Independence

In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

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 from...
Determination of Expected Frequency01:08

Determination of Expected Frequency

Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
Law of Independent Assortment02:03

Law of Independent Assortment

While Mendel’s Law of Segregation states that the two alleles for one gene are separated into different gametes, a different question of how different genes are inherited remains. For example, is the gene for tall plants inherited with the gene for green peas? Mendel asked this question by experimenting with a dihybrid cross; a cross in which both parents are homozygous for two distinct traits resulting in an F1 generation that are heterozygous for both traits.
Law of Independent Assortment02:03

Law of Independent Assortment

While Mendel’s Law of Segregation states that the two alleles for one gene are separated into different gametes, a different question of how different genes are inherited remains. For example, is the gene for tall plants inherited with the gene for green peas? Mendel asked this question by experimenting with a dihybrid cross; a cross in which both parents are homozygous for two distinct traits resulting in an F1 generation that are heterozygous for both traits.
Random Variables01:09

Random Variables

A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...

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Related Experiment Video

Updated: Jun 18, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

The conditional independences between variables derived from two independent identically distributed Markov random

Alun Thomas1

  • 1Genetic Epidemiology, University of Utah, Salt Lake City, UT 84108, USA. alun@genepi.med.utah.edu

Mathematical Medicine and Biology : a Journal of the IMA
|November 28, 2009
PubMed
Summary

This study extends graph theory for Markov models to arbitrary forests, proving equivalence between ordered and unordered variables. This finding simplifies estimating graphical models for genetic linkage disequilibrium.

Related Experiment Videos

Last Updated: Jun 18, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Area of Science:

  • Graph Theory and Statistical Modeling
  • Computational Biology and Genetics

Background:

  • Conditional independence graphs are crucial for understanding complex dependencies in statistical models.
  • First-order Markov models provide a framework for sequential data analysis.
  • Estimating graphical models for genetic linkage disequilibrium is vital for understanding gene associations.

Purpose of the Study:

  • To extend the equivalence of conditional independence graphs for ordered and unordered vector random variables from first-order Markov models.
  • To generalize this equivalence to arbitrary forests.
  • To provide theoretical justification for using genotypes instead of haplotypes in certain genetic linkage analyses.

Main Methods:

  • Theoretical extension of graph equivalence results for Markov models.
  • Application of graph theory principles to arbitrary forest structures.
  • Analysis of conditional independence structures in genetic data.

Main Results:

  • Established the equivalence of conditional independence graphs for ordered and unordered vector random variables in first-order Markov models, extended to arbitrary forests.
  • Demonstrated that the conditional independence structure remains invariant whether considering ordered or unordered variables.
  • Provided a theoretical basis for simplifying genetic data analysis by showing when genotype information suffices.

Conclusions:

  • The theoretical equivalence simplifies the estimation of graphical models, particularly in the context of genetic linkage disequilibrium.
  • The findings explain why, in terms of conditional independence, the choice between haplotypes and genotypes can be inconsequential.
  • This work offers a more efficient approach to analyzing genetic associations by leveraging graph theory.