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Summary
This summary is machine-generated.

Pearson's chi-squared (χ2) test can be used as an exact test for any sample size, making Fisher's exact test unnecessary. Routinely using an exact test ensures a more reliable statistical analysis.

Keywords:
2 × 2 tableCochran's rule of thumbFisher's exact testPearson's χ2 test

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Area of Science:

  • Statistics
  • Biostatistics

Background:

  • Pearson's asymptotic chi-squared (χ2) test is commonly used for binary data comparison between two groups.
  • Fisher's exact test is often substituted for Pearson's χ2 test when sample sizes or expected frequencies are small.
  • Current practices involve data-dependent switching between tests, which is statistically unusual.

Purpose of the Study:

  • To advocate for the routine use of exact tests for comparing binary data.
  • To highlight the unnecessary nature of switching statistical tests based on data characteristics.
  • To promote a more consistent and reliable analytical approach.

Main Methods:

  • The study discusses the statistical properties of Pearson's χ2 test and Fisher's exact test.
  • It emphasizes that Pearson's χ2 test can be performed as an exact test for all sample sizes.
  • The analysis critiques the common practice of conditional test selection.

Main Results:

  • Pearson's χ2 test, when implemented exactly, is suitable for all sample sizes and expected frequencies.
  • The practice of switching to Fisher's exact test based on data is statistically unnecessary and problematic.
  • Using an exact test routinely simplifies analysis and enhances reliability.

Conclusions:

  • Routinely employing an exact test, such as Pearson's χ2 test performed exactly, is recommended for comparing binary data.
  • This approach eliminates the ambiguity and unreliability associated with data-dependent test selection.
  • Adopting this method allows for pre-specification of the test, leading to a more robust analysis.