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Contingency Table

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...

Decision Making: P-value Method

Decision Making: P-value Method

The process of hypothesis testing based on the P-value method includes calculating the P- value using the sample data and interpreting it.
First, a specific claim about the population parameter is proposed. The claim is based on the research question and is stated in a simple form. Further, an opposing statement to the claim is also stated. These statements can act as null and alternative hypotheses: a null hypothesis would be a neutral statement while the alternative hypothesis can...

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:

Inductive Reasoning

Inductive Reasoning

Inductive reasoning is a form of logical thinking that uses related observations to arrive at a general conclusion. It is uncertain and operates in degrees to which the conclusions are credible. As such, inductive arguments can be weak or strong, rather than valid or invalid, and conclusions can be used to formulate testable, falsifiable hypotheses.
Inductive reasoning is common in descriptive science. A life scientist makes observations and records them. This data can be qualitative or...

Deductive Reasoning

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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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Related Experiment Video

Updated: Jun 2, 2025

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Measuring the Subjective Value of Risky and Ambiguous Options using Experimental Economics and Functional MRI Methods

Published on: September 19, 2012

Pitting base rate driven heuristics against conditional reasoning in multivariate contingency assessment.

Klaus Fiedler¹, Florian Kutzner²

¹Heidelberg University, Department of Psychology.

Journal of Experimental Psychology. Learning, Memory, and Cognition

|January 13, 2025

Summary

Pseudocontingencies (PCs), a simpler cognitive mechanism, often override complex conditional probabilities in judging attribute relationships. This finding is crucial for understanding decision-making and cognitive biases.

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Area of Science:

Cognitive Psychology
Ecological Rationality

Background:

Contingency assessment is key to adaptive cognition and ecological rationality.
Existing theories rely on subjective conditional probabilities, which are cognitively demanding.

Purpose of the Study:

To investigate the role of pseudocontingencies (PCs) as an alternative to conditional probabilities in contingency assessment.
To examine PC dominance over conditional probabilities, especially in complex multivariate settings.

Main Methods:

Experiments 1 and 1a manipulated PCs and conditional probabilities orthogonally.
Experiment 2 explored the dissociation between contingency judgments and evaluative conditioning.

Main Results:

Pseudocontingencies were found to dominate conditional probabilities in judgments.
This dominance was particularly pronounced in multivariate tasks requiring multiple pairwise contingency assessments.
Contingency judgments were dissociated from evaluative conditioning.

Conclusions:

Pseudocontingencies offer a cognitively simpler mechanism for assessing attribute relationships.
PC dominance highlights potential biases in human judgment, particularly in complex decision-making scenarios.