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Related Concept Videos

Introduction to Test of Independence01:21

Introduction to Test of Independence

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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.
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
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Hypothesis Test for Test of Independence01:16

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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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The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can...
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Determination of Expected Frequency

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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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Expected Frequencies in Goodness-of-Fit Tests01:19

Expected Frequencies in Goodness-of-Fit Tests

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A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n)  to the number of categories (k).
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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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A Conditional Mutual Information Estimator for Mixed Data and an Associated Conditional Independence Test.

Lei Zan1,2, Anouar Meynaoui1, Charles K Assaad2

  • 1Department of Mathematics, Information and Communication Sciences, Université Grenoble Alpes, CNRS, Grenoble INP, LIG, 38000 Grenoble, France.

Entropy (Basel, Switzerland)
|September 23, 2022
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Summary

This study introduces CMIh for estimating conditional mutual information and LocAT for detecting conditional independence in mixed data, improving analysis for complex datasets.

Keywords:
conditional independence testingconditional mutual informationmixed datapermutation tests

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Area of Science:

  • Statistics
  • Machine Learning
  • Data Science

Background:

  • Mixed data, comprising both quantitative and qualitative variables, presents unique analytical challenges.
  • Existing methods for estimating conditional mutual information and detecting independence are often limited to purely quantitative or qualitative data.
  • Accurate analysis of mixed data is crucial for various fields, including bioinformatics and social sciences.

Purpose of the Study:

  • To develop novel statistical methods for analyzing mixed data.
  • To propose a new approach for estimating conditional mutual information (CMIh) that handles both quantitative and qualitative components.
  • To introduce a new local permutation test (LocAT) specifically designed for detecting conditional (in)dependence in mixed data.

Main Methods:

  • The study proposes CMIh, a novel method for estimating conditional mutual information by integrating existing approaches for qualitative and quantitative data.
  • A new local adaptive test (LocAT), a local permutation test, is introduced to effectively analyze mixed data.
  • Experimental validation was performed to assess the performance of the proposed methods.

Main Results:

  • The proposed CMIh method demonstrates accurate estimation of conditional mutual information for mixed data.
  • The LocAT method effectively detects conditional (in)dependence in mixed data.
  • Experimental results confirm the robust performance of both CMIh and LocAT on mixed datasets.

Conclusions:

  • CMIh and LocAT are effective and well-adapted tools for analyzing mixed data.
  • These methods advance the capabilities for conditional mutual information estimation and conditional independence testing in complex, heterogeneous datasets.
  • The developed methods offer significant improvements for researchers working with mixed-type variables.