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Related Concept Videos

Contingency Table01:29

Contingency Table

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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...
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Introduction to Test of Independence01:21

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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.
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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:
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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...
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There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
When the null and alternative hypotheses are stated, it is observed that the null hypothesis is a neutral statement against which the alternative hypothesis is tested. The alternative hypothesis is a claim that instead has a certain direction. If the null hypothesis claims that p = 0.5, the alternative hypothesis would be an opposing statement to this and can be put either p > 0.5, p < 0.5, or p...
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The process of hypothesis testing based on the traditional method includes calculating the critical value, testing the value of the test statistic using the sample data, and interpreting these values.
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An AIC-type information criterion evaluating theory-based hypotheses for contingency tables.

Yasin Altinisik1, Roy S Hessels2, Caspar J Van Lissa3

  • 1Department of Statistics, Sinop University, Osmaniye Mahallesi, Selanik Caddesi (Kuzey Kampüs), No:52G, 57000, Sinop, Türkiye.

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|January 22, 2025
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Summary

This study introduces GORICA, a new method for analyzing complex relationships in high-dimensional contingency tables. GORICA simplifies hypothesis testing with equality and inequality constraints, overcoming limitations of traditional log-linear models.

Keywords:
(In)equality constraintsAICContingency tablesGORICATheory-based hypotheses

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Area of Science:

  • Statistics
  • Data Analysis
  • Statistical Modeling

Background:

  • Evaluating theory-based hypotheses in contingency tables presents challenges.
  • Log-linear models often lack the capacity to handle complex relationships and inequality restrictions.
  • High-dimensional tables with sparse or empty cells complicate parameter estimation and interpretation.

Purpose of the Study:

  • To propose a novel method simplifying the evaluation of theory-based hypotheses in high-dimensional contingency tables.
  • To address limitations of traditional log-linear models, including handling inequality constraints and sparse data.
  • To introduce an AIC-type information criterion, GORICA, for evaluating hypotheses with mixed constraints.

Main Methods:

  • Development of the GORICA (Generalized Order Restricted Information Criterion for Analysis) method.
  • Specification of theory-based hypotheses using equality and/or inequality constraints on cell probabilities.
  • Evaluation of GORICA's performance through a simulation study on contingency tables.
  • Application of the method to two empirical examples.

Main Results:

  • The proposed method effectively simplifies the evaluation of complex hypotheses in high-dimensional contingency tables.
  • GORICA demonstrates robust performance in simulation studies, handling sparse data and mixed constraints.
  • The method enhances interpretability compared to traditional log-linear approaches.

Conclusions:

  • GORICA offers a powerful and flexible alternative for analyzing theory-based hypotheses in challenging contingency table data.
  • The method successfully integrates equality and inequality constraints, improving upon existing statistical approaches.
  • Empirical examples showcase the practical utility and effectiveness of GORICA in real-world research.