Approximating power of the unconditional test

Abstract

We provide a simple and good approximation of power of the unconditional test for two correlated binary variables. Suissa and Shuster (1991) described the exact unconditional test. The most commonly used statistical test in this setting, McNemar's test, is exact conditional on the sum of the discordant pairs. Although asymptotically the conditional and unconditional versions coincide, a long‐standing debate surrounds the choice between them. Several power approximations have been studied for both methods (Miettinen, 1968; Bennett and Underwood, 1970; Connett, Smith, and Mc Hugh, 1987; Connor, 1987; Connor, 1987; Suissa and Shuster, 1991; Lachenbruch, 1992; Lachin, 1992). For the unconditional approach most existing power approximations use the Gaussian distribution, while the accurate (“exact”) method is computationally burdensome.

A new approximation uses the F statistic corresponding to a paired‐data T test computed from the difference scores of the binary outcomes. Enumeration of all possible 2 x 2 tables for small sample sizes allowed evaluation of both test size and power. The new approximation compares favorably to others due to the combination of ease of use and accuracy.

Keywords:

• 2 x 2 table
• McNemar's Test