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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...
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...
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)...
Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data01:16

Statistical Inference Techniques in Hypothesis Testing: Parametric Versus Nonparametric Data

Statistical inference techniques, paramount in hypothesis testing, differentiate into two broad categories: parametric and nonparametric statistics.
Parametric statistics, as the name suggests, assumes that data follow a specific distribution, often a normal distribution. This assumption enables robust hypothesis testing and estimation. Parametric methods, like the Student's t-test or Goodness-of-fit test, are frequently employed in biostatistics due to their robustness. For instance, comparing...

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Related Experiment Video

Updated: Jul 15, 2026

Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects
08:13

Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects

Published on: May 10, 2019

Bayesian methods for the analysis of inequality constrained contingency tables.

Olav Laudy1, Herbert Hoijtink

  • 1Department of Methodology and Statistics, Utrecht University, The Netherlands. o.laudy@fss.uu.nl

Statistical Methods in Medical Research
|May 9, 2007
PubMed
Summary

This study introduces a Bayesian approach for analyzing contingency tables with inequality constraints. It enables estimation, hypothesis testing, and model selection for cell probabilities and odds ratios using a Gibbs sampler.

Related Experiment Videos

Last Updated: Jul 15, 2026

Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects
08:13

Using the Race Model Inequality to Quantify Behavioral Multisensory Integration Effects

Published on: May 10, 2019

Area of Science:

  • Statistics
  • Bayesian Inference
  • Contingency Table Analysis

Background:

  • Inequality constraints are common in statistical modeling but challenging to analyze.
  • Existing methods for contingency tables may not adequately handle complex inequality constraints.
  • Bayesian methods offer a flexible framework for incorporating prior information and quantifying uncertainty.

Purpose of the Study:

  • To present a comprehensive Bayesian methodology for analyzing inequality constrained models in contingency tables.
  • To develop methods for estimating cell probabilities, testing hypotheses, and selecting models under inequality constraints.
  • To explore constraints on various forms of odds ratios, including conditional, local, global, continuation, and cumulative.

Main Methods:

  • A Bayesian framework is employed, utilizing a Gibbs sampler to generate a discrete posterior distribution of parameters.
  • Credibility regions for functions of cell probabilities are constructed from the discrete posterior representation.
  • Posterior model probabilities and posterior predictive checks are used for model selection and hypothesis testing, respectively.

Main Results:

  • The proposed methodology effectively handles inequality constraints on cell probabilities and various odds ratios.
  • The Gibbs sampler provides a practical way to obtain the posterior distribution for complex models.
  • Credibility regions and posterior model probabilities allow for robust inference and model comparison.

Conclusions:

  • The developed Bayesian methodology provides a powerful and flexible tool for analyzing inequality constrained contingency table models.
  • This approach facilitates accurate estimation, hypothesis testing, and model selection in complex scenarios.
  • The illustrated examples demonstrate the practical applicability and effectiveness of the proposed Bayesian framework.