APPROXIMATING POWER OF THE UNCONDITIONAL TEST FOR CORRELATED BINARY PAIRS

Area of Science:

• Biostatistics
• Statistical Methods
• Correlated Binary Data Analysis

Background:

• McNemar's test is commonly used for paired binary data but is conditional.
• Debate exists regarding conditional vs. unconditional tests for correlated binary variables.
• Existing power approximations for unconditional tests often rely on Gaussian distributions and can be computationally intensive.

Purpose of the Study:

• To develop a simple and accurate approximation for the power of the unconditional test for two correlated binary variables.
• To address the computational burden of exact unconditional methods.
• To offer a practical alternative to existing power approximation methods.

Main Methods:

• A novel approximation utilizing the F statistic from a paired-data T test on difference scores.
• Evaluation of test size and power through enumeration of all possible 2x2 tables for small sample sizes.
• Comparison of the new approximation against existing methods.

Main Results:

• The proposed approximation demonstrates favorable performance compared to existing methods.
• The new approximation combines ease of use with accuracy.
• The method was validated using enumeration for small sample sizes.

Conclusions:

• A simple and accurate approximation for unconditional test power in correlated binary data is presented.
• This new method offers a practical and computationally efficient solution.
• The approximation shows promise for statistical analysis of paired binary outcomes.