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

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:

Bias

Bias

Bias refers to any tendency that prevents a question from being considered unprejudiced. In research, bias occurs when one outcome or answer is selected or encouraged over others in sampling or testing. Bias can occur during any research phase, including study design, data collection, analysis, and publication.
In statistics, a sampling bias is created when a sample is collected from a population, and some members of the population are not as likely to be chosen as others (remember, each member...

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...

Testing a Claim about Population Proportion

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A complete procedure for testing a claim about a population proportion is provided here.
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...

Hypothesis: Accept or Fail to Reject?

Hypothesis: Accept or Fail to Reject?

The outcome of any hypothesis testing leads to rejecting or not rejecting the null hypothesis. This decision is taken based on the analysis of the data, an appropriate test statistic, an appropriate confidence level, the critical values, and P-values. However, when the evidence suggests that the null hypothesis cannot be rejected, is it right to say, 'Accept' the null hypothesis?
There are two ways to indicate that the null hypothesis is not rejected. 'Accept' the null...

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Related Experiment Video

Updated: Apr 1, 2026

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

Using alien coins to test whether simple inference is Bayesian.

Peter Cassey¹, Guy E Hawkins², Chris Donkin³

¹School of Psychology, University of Newcastle.

Journal of Experimental Psychology. Learning, Memory, and Cognition

|October 14, 2015

Summary

This summary is machine-generated.

Human reasoning often deviates from statistically optimal Bayesian inference. Quantitative comparisons reveal most individuals struggle with Bayes

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Creating Objects and Object Categories for Studying Perception and Perceptual Learning

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Published on: November 2, 2012

Area of Science:

Cognitive science
Computational neuroscience
Psychology

Background:

Reasoning and inference are fundamental cognitive processes.
Bayesian inference models propose statistically optimal decision-making.
Previous research often aggregates data, masking individual variability.

Purpose of the Study:

To quantitatively compare individual human inference with Bayesian inference models.
To evaluate the adherence of human decision-making to Bayes' rule at the individual level.
To assess the generalizability of Bayesian models across diverse cognitive tasks.

Main Methods:

Employed a simplified experimental design across three studies.
Recruited over 13,000 participants for the studies.
Collected individual prior and posterior probability inferences regarding coin outcomes.

Main Results:

The majority of participants demonstrated inferences inconsistent with Bayes' rule.
Adherence to Bayes' rule was observed only in the simplest experimental condition.
A significant proportion of individuals failed to comply with Bayes' rule even in the simplest task.

Conclusions:

Human reasoning and inference show significant deviations from Bayesian predictions.
Bayesian models may not fully capture individual cognitive processes in probabilistic reasoning.
Emphasizes the need for individual-level quantitative comparisons in cognitive modeling.