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Related Concept Videos

Contingency Table01:29

Contingency Table

4.8K
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...
4.8K
Introduction to Test of Independence01:21

Introduction to Test of Independence

3.1K
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:
3.1K
Determination of Expected Frequency01:08

Determination of Expected Frequency

2.7K
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...
2.7K
Hypothesis Test for Test of Independence01:16

Hypothesis Test for Test of Independence

8.3K
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)...
8.3K
Factorial Design02:01

Factorial Design

15.3K
Factorial Analysis is an experimental design that applies Analysis of Variance (ANOVA) statistical procedures to examine a change in a dependent variable due to more than one independent variable, also known as factors. Changes in worker productivity can be reasoned, for example, to be influenced by salary and other conditions, such as skill level. One way to test this hypothesis is by categorizing salary into three levels (low, moderate, and high) and skills sets into two levels (entry level...
15.3K
Fisher's Exact Test01:08

Fisher's Exact Test

1.4K
Fisher's exact test is a statistical significance test widely used to analyze 2x2 contingency tables, particularly in situations where sample sizes are small. Unlike the chi-squared test, which approximates P-values and assumes minimum expected frequencies of at least five in each cell, Fisher's exact test calculates the exact probability (P-value) of observing the data or more extreme results under the null hypothesis. This feature makes it especially valuable when the assumptions of...
1.4K

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Related Experiment Video

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A Real-world What-Where-When Memory Test
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[A factor analysis method for contingency table data with unlimited multiple choice questions].

Hideki Toyoda, Reina Haiden, Saori Kubo

    Shinrigaku Kenkyu : the Japanese Journal of Psychology
    |March 12, 2016
    PubMed
    Summary

    This study introduces a novel factor analysis method for multiple-choice survey data. The approach effectively analyzes contingency tables, offering interpretable factors for psychological research.

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    Area of Science:

    • Psychometrics
    • Statistical Modeling

    Context:

    • Analyzing data from unlimited multiple-choice questions presents unique statistical challenges.
    • Traditional factor analysis models may not be optimal for contingency table data derived from such questions.

    Purpose:

    • To propose a new factor analysis method tailored for contingency tables from unlimited multiple-choice questions.
    • To apply a factor analysis model to the logit of selection probabilities, assuming binomial distribution for cell elements.

    Summary:

    • The method utilizes scree plots and Watanabe-Akaike Information Criterion (WAIC) for factor determination.
    • Item selection is guided by standardized residuals, standardized sample differences, and proportion ratios.
    • The technique was validated using product impression data for advertised chips and energy drinks.

    Impact:

    • Demonstrates compatibility and interpretability comparable to conventional factor analysis models.
    • Highlights the method's utility in psychological studies employing unlimited multiple-choice questionnaires.
    • Provides a robust tool for analyzing complex categorical data in research settings.