Recommended tests for association in 2 x 2 tables.

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Traditional methods like Pearson's chi-squared and Fisher's exact tests are standard for analyzing 2x2 contingency tables.
• Fisher's exact test, while widely used, has limitations in power and significance level preservation for certain sample sizes.

Purpose of the Study:

• To evaluate the comparative performance of different statistical tests for association in 2x2 tables.
• To advocate for the increased adoption of unconditional tests and the mid-p adjustment in statistical practice.

Main Methods:

• The study reviews the properties and performance of asymptotic Pearson's chi-squared test, Fisher's exact test, unconditional tests, and Fisher's exact test with mid-p adjustment.
• Computational demands, significance level preservation, and statistical power are key comparison metrics.

Main Results:

• Unconditional tests maintain significance levels and offer greater power than Fisher's exact test, especially in small to moderate samples.
• The computational burden of unconditional tests is no longer a barrier due to available software.
• Fisher's exact test with mid-p adjustment yields similar results to unconditional tests.

Conclusions:

• Unconditional tests and the mid-p adjustment are statistically superior and should be preferred over the traditional Fisher's exact test.
• The choice of statistical test for 2x2 tables should be based on its inherent merits and suitability for the specific application.
• The traditional Fisher's exact test is rarely the optimal choice and should be largely avoided in favor of more robust methods.