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Related Concept Videos

How Data are Classified: Categorical Data01:11

How Data are Classified: Categorical Data

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A variable, usually notated by capital letters such as X and Y, is a characteristic or measurement that can be determined for each member of a population. Data are the actual values of variables. They may be numbers, or they may be words. Datum is a single value.
Data are classified based on whether they are measurable or not. Categorical data cannot be measured; instead, it can be divided into categories. For example, if Y denotes a person's party affiliation, some examples of Y include...
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One-Way ANOVA01:18

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One-way ANOVA analyzes more than three samples categorized by one factor. For example, it can compare the average mileage of sports bikes. Here, the data is categorized by one factor - the company. However, one-way ANOVA cannot be used to simultaneously compare the sample mean of three or more samples categorized by two factors. An example of two factors would be sports bikes from different companies driven in different terrains, such as a desert or snowy landscape. Here, two-way ANOVA is used...
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Two-Way ANOVA01:17

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The two-way ANOVA is an extension of the one-way ANOVA. It is a statistical test performed on three or more samples categorized by two factors - a row factor and a column factor. Ronald Fischer mentioned it in 1925 in his book 'Statistical Methods for Researchers.'
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How Data are Classified: Numerical Data00:59

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Data that are countable or measurable in specific units are called numerical or quantitative data. Quantitative data are always numbers. Quantitative data are the result of counting or measuring the attributes of a population. Amount of money, pulse rate, weight, number of people living in a town, and number of students who opt for statistics are examples of quantitative data.
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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...
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The chi-square test is a statistical hypothesis test. It is used to check whether there is a significant difference between an expected value and an observed value. In the context of genetics, it enables us to either accept or reject a hypothesis, based on how much the observed values deviate from the expected values.
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Related Experiment Video

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Mimicking Complexity of Structured Data Matrix's Information Content: Categorical Exploratory Data Analysis.

Fushing Hsieh1, Elizabeth P Chou2, Ting-Li Chen3

  • 1Department of Statistics, University of California at Davis, Davis, CA 95616, USA.

Entropy (Basel, Switzerland)
|June 2, 2021
PubMed
Summary

Categorical Exploratory Data Analysis (CEDA) with mimicking visualizes complex data structures across multiple scales. This method enhances scientific reliability and clarifies feature importance in machine learning models.

Keywords:
contingency-kD-latticeheterogeneityhigh order structural dependencymutual conditional entropy matrixprincipal component analysis (PCA)

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Area of Science:

  • Data Science
  • Computational Statistics
  • Information Theory

Background:

  • Data matrices contain complex information, often obscured by heterogeneity and multiscale dependencies.
  • Existing methods may struggle to fully capture intricate structural relationships within diverse data types.
  • Understanding data complexity is crucial for reliable scientific inference and ethical AI.

Purpose of the Study:

  • To introduce Categorical Exploratory Data Analysis (CEDA) with mimicking for exploring complex information content in data matrices.
  • To visualize multiscale structural dependencies and heterogeneity within categorical, discrete, and continuous data.
  • To enhance data visualization for scientific reliability and clarify feature importance in machine learning.

Main Methods:

  • CEDA utilizes histograms for categorical features and a mutual conditional entropy matrix for order-2 dependence.
  • Higher-order dependencies (k>=3) are visualized through permuted contingency-kD-lattice heatmaps.
  • A mimicking protocol simulates heatmap series, preserving structural dependency from global to fine scales, with PCA for continuous features.

Main Results:

  • The method reveals visible and explainable serial multiscale structural dependency and heterogeneity.
  • Heatmap series generated by growing k display global and large-scale structural dependencies.
  • The mimicking protocol successfully preserves structural dependency across scales, adhering to observed categorical patterns.

Conclusions:

  • CEDA with mimicking offers enhanced data visualization, revealing deterministic and stochastic structures at different scales.
  • It clarifies the predictive power of covariate feature groups on response features in machine learning and statistics.
  • This approach contributes to the social justice of AI by assessing data matrix completeness and potential biases.