What is the difference between Fisher's exact test and Chi-square (χ²) test?

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From the Guidelines

The Fisher's exact test should be used instead of the chi-square test when sample sizes are small, particularly when expected cell counts are less than 5. While both tests evaluate relationships between categorical variables, Fisher's test provides more accurate results with small samples because it calculates exact probabilities rather than relying on approximations 1. The chi-square test is appropriate for larger datasets (generally when all expected cell counts exceed 5) and is computationally simpler. Fisher's test becomes computationally intensive with large samples but is more reliable for 2×2 contingency tables with limited data. The chi-square test requires fewer assumptions about sample size but may produce unreliable results with sparse data. When analyzing categorical data, first check your expected cell counts—if any fall below 5, Fisher's test is the better choice; otherwise, the chi-square test is typically sufficient and widely accepted in research 1.

Some key points to consider when choosing between the Fisher's exact test and the chi-square test include:

  • Sample size: Fisher's exact test is preferred for small sample sizes, while the chi-square test is suitable for larger datasets.
  • Expected cell counts: If any expected cell counts are less than 5, Fisher's exact test is the better choice.
  • Computational simplicity: The chi-square test is computationally simpler, but Fisher's exact test provides more accurate results with small samples.
  • Research guidelines: Both tests are widely accepted in research, but it is essential to choose the most appropriate test based on the specific research question and data characteristics, as recommended by guidelines for statistical reporting in medical journals 1.

In real-life clinical medicine, it is crucial to prioritize the most accurate and reliable test to ensure that results are valid and generalizable. By considering the sample size, expected cell counts, and computational simplicity, researchers and clinicians can make informed decisions about which test to use, ultimately improving the quality of research and patient care.

From the Research

Statistical Tests for Comparing Data

  • The choice of statistical test depends on the type and distribution of variables being compared 2
  • For categorical variables, the χ2 test is used, unless cell counts are less than five, in which case the Fisher exact test is used 2

Comparison of Fisher Test and Chi Square

  • The Fisher exact test is used when cell counts are less than five, while the χ2 test is used for larger cell counts 2
  • Both tests are used to assess for overall differences between two or more groups, but individual pair comparison tests and adjustments for multiple comparisons are necessary to identify differences between specific groups 2

Application of Statistical Tests in Medical Research

  • Statistical tests are essential in medical research to compare data and make inferences about a population of interest 3, 4
  • A basic understanding of statistical significance and the type and distribution of variables is necessary to select the appropriate statistical test 2, 3

Limitations and Considerations

  • The choice of statistical test depends on various factors, including the study design, data distribution, and sample size 2, 4
  • Clinicians and researchers should be aware of the assumptions, strengths, and limitations of different statistical tests to interpret research datasets accurately 4

References

Guideline

Guideline Directed Topic Overview

Dr.Oracle Medical Advisory Board & Editors, 2025

Research

Basics of Statistical Comparisons.

Indian pediatrics, 2021

Professional Medical Disclaimer

This information is intended for healthcare professionals. Any medical decision-making should rely on clinical judgment and independently verified information. The content provided herein does not replace professional discretion and should be considered supplementary to established clinical guidelines. Healthcare providers should verify all information against primary literature and current practice standards before application in patient care. Dr.Oracle assumes no liability for clinical decisions based on this content.

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