Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Contingency Table01:29

Contingency Table

A contingency table provides a way of portraying data that can facilitate calculating probabilities. It is a method of displaying a frequency distribution as a table with rows and columns to show how two variables may be dependent (contingent) upon each other; The table helps determine conditional probabilities quite quickly and can help systematically organize, analyze and quantify data. The table displays sample values concerning two variables that may be dependent or contingent on one...
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...
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:
Hypothesis Test for Test of Independence01:16

Hypothesis Test for Test of Independence

The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are:
H0: The two variables (factors)...
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...
McNemar's Test01:23

McNemar's Test

McNemar's Test is a nonparametric statistical test used to determine if there is a significant difference in proportions between two related groups when the outcome is binary (e.g., yes/no, success/failure). It is beneficial when we have paired data, such as pre-test/post-test designs, where the same subjects are measured under two different conditions. The test is named after the statistician Quinn McNemar, who introduced it in 1947. It is commonly used in situations where subjects are...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Histomorphologic characteristics of abdominal aortic aneurysm samples are similar in abdominal-only vs thoracoabdominal involvement.

JVS-vascular science·2026
Same author

Effectiveness and feasibility of short-course simulator training for robotic surgery novices - a randomized controlled trial (FastSim trial).

Innovative surgical sciences·2026
Same author

IMPERATIVE: Harnessing male peer networks to enhance engagement with HIV prevention: A large-scale cluster randomised trial to increase HIV self-testing and PrEP uptake among men in Eastern Zimbabwe.

Research square·2026
Same author

NOX4 signatures in human abdominal aortic aneurysm reveal links to vascular cell plasticity, extracellular matrix remodeling and inflammation.

Free radical biology & medicine·2026
Same author

Combined Preoperative Risk Score Including sCD40, Leukocytes, and BMI Predicts Pancreas-Specific Complications After Pancreatic Cancer Surgery.

Annals of surgical oncology·2026
Same author

ASO Visual Abstract: Combined Preoperative Risk Score Including sCD40, Leukocytes, and BMI Predicts Pancreas-Specific Complications After Pancreatic Cancer Surgery.

Annals of surgical oncology·2026
Same journal

A Bayesian method for analyzing combinations of continuous, ordinal, and nominal categorical data with missing values.

Journal of multivariate analysis·2026
Same journal

Hierarchical structure-guided high-dimensional multi-view clustering.

Journal of multivariate analysis·2026
Same journal

Quadratic inference with dense functional responses.

Journal of multivariate analysis·2025
Same journal

Graph-constrained Analysis for Multivariate Functional Data.

Journal of multivariate analysis·2025
Same journal

From multivariate to functional data analysis: fundamentals, recent developments, and emerging areas.

Journal of multivariate analysis·2024
Same journal

Modeling the Cholesky factors of covariance matrices of multivariate longitudinal data.

Journal of multivariate analysis·2024
See all related articles

Related Experiment Video

Updated: May 29, 2026

RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans
11:09

RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans

Published on: July 17, 2021

Relational models for contingency tables.

Anna Klimova1, Tamás Rudas, Adrian Dobra

  • 1Department of Statistics, University of Washington, Box 355845, Seattle WA 98195-4322, USA; klimova@u.washington.edu.

Journal of Multivariate Analysis
|September 16, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces coordinate-free multiplicative models for contingency tables, generalizing log-linear models. It establishes conditions for maximum likelihood estimates and explores likelihood equivalences, offering new insights into statistical modeling.

More Related Videos

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

An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Related Experiment Videos

Last Updated: May 29, 2026

RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans
11:09

RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans

Published on: July 17, 2021

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

An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Area of Science:

  • Statistics
  • Statistical Modeling
  • Categorical Data Analysis

Background:

  • Log-linear models are widely used for analyzing contingency tables.
  • Existing models can be restrictive and coordinate-dependent.
  • There is a need for more general and flexible statistical models for categorical data.

Purpose of the Study:

  • To introduce and explore general multiplicative models for complete and incomplete contingency tables.
  • To develop coordinate-free models that generalize log-linear and other existing models.
  • To investigate conditions for the existence of maximum likelihood estimates and likelihood equivalences.

Main Methods:

  • Consideration of general multiplicative models for contingency tables.
  • Derivation of sufficient conditions for the existence of maximum likelihood estimates.
  • Analysis of the equivalence between multinomial and Poisson likelihoods.
  • Development of a mixed parameterization for models without an overall effect, utilizing non-homogeneous odds ratios.

Main Results:

  • The proposed models are coordinate-free and generalize existing statistical models.
  • Conditions for the existence of maximum likelihood estimates are established.
  • The equivalence between multinomial and Poisson likelihoods is shown to depend on the presence of an overall effect.
  • A novel mixed parameterization is presented for models lacking an overall effect, involving non-homogeneous odds ratios.

Conclusions:

  • The developed multiplicative models offer a flexible and coordinate-free approach to contingency table analysis.
  • The findings clarify the relationship between different likelihoods based on model specifications.
  • The study provides valuable tools and insights for researchers working with categorical data.