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Related Concept Videos

Contingency Table01:29

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...
Determination of Expected Frequency01:08

Determination of Expected Frequency

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...
Introduction to Test of Independence01:21

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:
Probability in Statistics01:14

Probability in Statistics

Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
Probability Distributions01:32

Probability Distributions

The probability of a random variable x  is the likelihood of its occurrence. A probability distribution represents the probabilities of a random variable using a formula, graph, or table. There are two types of probability distribution– discrete probability distribution and continuous probability distribution.
A discrete probability distribution is a probability distribution of discrete random variables. It can be categorized into binomial probability distribution and Poisson probability...
Hypothesis Test for Test of Independence01:16

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:
H0: The two variables (factors)...

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Contingency and its two indices within conditional probability analysis.

J S Watson

    The Behavior Analyst
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    PubMed
    Summary
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    Conditional probability analysis offers the most powerful method for detecting behavior-stimulus contingencies. This approach uses forward and backward probabilities, crucial for understanding learning in animals and humans.

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    Area of Science:

    • Behavioral Psychology
    • Cognitive Science
    • Machine Learning

    Background:

    • Understanding the relationship between behavior and its consequences is fundamental to learning theory.
    • Several theoretical frameworks exist for detecting these contingencies, including contiguity, correlation, conditional probability, and logical implication.

    Purpose of the Study:

    • To evaluate the statistical power of different theoretical bases for detecting behavioral contingencies.
    • To introduce conditional probability analysis as a superior method, highlighting its dual indices.

    Main Methods:

    • Review and theoretical analysis of four bases for contingency detection: contiguity, correlation, conditional probability, and logical implication.
    • Examination of evidence regarding the efficacy of these bases in animal and human learning, as well as in artificial neural networks.

    Main Results:

    • Conditional probability analysis is identified as the statistically most powerful method for detecting contingencies.
    • This method provides two key indices: forward time probability (reinforcement follows behavior) and backward time probability (behavior precedes reinforcement).
    • Both indices are relevant to animal learning, but their salience differs in humans and artificial neural networks.

    Conclusions:

    • Conditional probability analysis, with its forward and backward indices, offers a robust framework for understanding contingency detection.
    • Human contingency detection may develop progressively, potentially moving from simpler concepts like contiguity and correlation to more complex conditional probabilities and logical implication.