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This study reviews Chi-square (χ(2)) tests for analyzing categorical data in contingency tables. It highlights Pearson

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Area of Science:

  • Statistics
  • Biostatistics
  • Data Analysis

Background:

  • Categorical variables are frequently analyzed using counts and frequencies.
  • Contingency tables (r × c) are standard for organizing categorical data.
  • The Chi-square (χ(2)) distribution is fundamental for analyzing categorical variables.

Purpose of the Study:

  • To provide an overview of various Chi-square (χ(2)) tests used in statistical analysis.
  • To differentiate the applications of common χ(2) tests, including Pearson's, McNemar's, Mantel-Haenszel, and Cochran's Q tests.
  • To explain the utility of Fisher's exact probability test as an alternative for small sample sizes.

Main Methods:

  • Review of established statistical tests for categorical data analysis.
  • Explanation of the principles behind Chi-square (χ(2)) distribution and its applications.
  • Comparison of different χ(2) tests based on data structure (independent vs. paired, dichotomous vs. ordered).

Main Results:

  • Pearson's χ(2) test is widely used for independent group comparisons.
  • Fisher's exact test is suitable for small sample sizes in 2x2 tables.
  • McNemar's χ(2) test and Cochran's Q test are used for paired or related proportions.

Conclusions:

  • Chi-square (χ(2)) tests are versatile tools for categorical data analysis.
  • The choice of test depends on the nature of the data and the research question.
  • P-values from χ(2) tests do not quantify association strength; relative risk or odds ratios are used for this.