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Introduction to Test of Independence

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:

Competition

Competition

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Decision Making: Traditional Method

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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Mechanistic Models: Compartment Models in Individual and Population Analysis

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Decision Making: P-value Method

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Hypothesis Test for Test of Independence

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:
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Related Experiment Video

Updated: May 14, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Disentangling decision models: from independence to competition.

Andrei R Teodorescu¹, Marius Usher

¹Department of Psychology, Tel-Aviv University, Ramat-Aviv, Israel. andreite@post.tau.ac.il

Psychological Review

|January 30, 2013

Summary

This summary is machine-generated.

Decision-making models were tested using computational and experimental studies. Findings suggest that decision processes are competitive, likely occurring at a late response stage, not an early input stage.

Related Experiment Videos

Last Updated: May 14, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Area of Science:

Cognitive Neuroscience
Computational Neuroscience
Decision Science

Background:

Numerous models explain neural mechanisms of value integration and decision-making in speeded tasks.
Models often disagree on whether choice mechanisms involve independent or competitive processing.

Purpose of the Study:

To compare five distinct decision-making models: independent race, input competition (normalized race, feed-forward inhibition), and response competition (max-minus-next diffusion, leaky competing accumulators).
To investigate the stage at which competition arises in decision-making processes.

Main Methods:

Conducted three combined computational and experimental studies manipulating task difficulty.
Constrained model parameters to prevent artificial data fitting and isolate model predictions.
Simulated response times under varying difficulty levels for each model class.

Main Results:

Independent models predict faster response times with increased difficulty.
Response competition models predict slower response times with increased difficulty.
Input competition models showed varied predictions depending on the specific model and conditions.

Conclusions:

Empirical and computational evidence supports intrinsically competitive decisional processes.
Competition in decision-making appears to occur at a late response stage rather than an early input stage.