A critical review of asymptotic methods for comparing two proportions by means of independent samples

Abstract

The test for comparing two proportions (based on the use of independent samples) is one of the best-known in statistics, and at the same time is the one that generates most disagreement, both in the asymptotic and non-asymptotic versions. The present article offers a critical review of the former, grouping them by "families", points out their theoretical relation to the latter, and details the main errors that have given rise to lop-sided arguments or have resulted in unsound conclusions. It also selects the optimal known versions (from the point of view mentioned) and their conditions of validity. Finally, it shows the main gaps that exist at present, and suggests how to solve them.

Keywords:

• Chi-squared test
• comparison of two proportions
• conditioned method
• correction for continuity
• Fisher's exact test
• 2×2 tables
• unconditioned method