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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.
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Hypothesis Test for Test of Independence

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Related Experiment Video

Updated: Sep 15, 2025

Application of Granger Causality Analysis of the Directed Functional Connection in Alzheimer's Disease and Mild Cognitive Impairment

Application of Granger Causality Analysis of the Directed Functional Connection in Alzheimer's Disease and Mild Cognitive Impairment

Published on: August 7, 2017

Independence-based causal discovery analysis reveals statistically non-significant regions to be functionally

Madison Lewis¹, Shaun Eack², Nicholas Theis³

¹Department of Bioengineering, Swanson School of Engineering, University of Pittsburgh, PA 15213.

Biorxiv : the Preprint Server for Biology

|July 16, 2025

Summary

Statistically non-significant brain regions causally interact with significant ones, challenging traditional fMRI analysis. This suggests silent brain networks play a role in psychopathology and cognition.

Keywords:

Network neuroscience causal discovery familial high-risk functional connectivity schizophrenia transdiagnostic approach

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Dynamic Inter-subject Functional Connectivity Reveals Moment-to-Moment Brain Network Configurations Driven by Continuous or Communication Paradigms

Dynamic Inter-subject Functional Connectivity Reveals Moment-to-Moment Brain Network Configurations Driven by Continuous or Communication Paradigms

Published on: March 21, 2019

Area of Science:

Neuroimaging
Computational Neuroscience
Psychiatry

Background:

Traditional fMRI analysis often overlooks statistically non-significant brain regions, assuming biological insignificance.
This study challenges this assumption by investigating causal interactions between significant (active network, AN) and non-significant (silent network, SN) brain regions.

Purpose of the Study:

To test the causal interactions between AN and SN.
To determine if these interactions influence psychopathology severity and working memory performance.

Main Methods:

Examined AN and SN during the N-BACK task in 25 individuals with familial risk for psychosis (FHR) and 37 controls.
Utilized the PC algorithm for causal discovery and analyzed connectivity of regions with highest alpha-centrality (HAC).

Main Results:

Identified causal connectivity between SN and AN, indicating mutual influence.
Found that specific HAC regions in both groups formed reciprocal circuits that causally increased magical ideation severity.

Conclusions:

Statistically non-significant brain regions causally interact with significant regions, suggesting they are not biologically unimportant.
Findings question the exclusive inclusion of significant regions in pathophysiological models and highlight the importance of causality analysis.