Unconditional Inferences on the Difference of Two Proportions in Cross-sectional Studies

Abstract

In order to analyse a 2 x 2 table it is usual to perform inferences (hypothesis test or interval of confidence) on the difference d = p2 - p1 between two independent proportions. To this end it has been customary to adopt the Fisher conditional method, but nowadays the unconditional method of Barnard is increasingly adopted. However, all the present unconditional inferences are based on a double-binomial model. This article performs these inferences - exact and asymptotic - under a multinomial model, which is the appropriate one when the data proceed from a cross-sectional survey. At http://www.ugr.es/-bioest/SG_ASO.EXE there is a program for performing the said unconditional tests that may be copied.

Evaluating the Performance of Simultaneous Stepwise Confidence Intervals for the Difference between two Poisson Rates

“…We also explored the potential benefits of the Pirie-Hamdan (Pirie & Hamdan, 1972) and Martin Andres-Tapia Garcia (Marin Andres & Tapia Garcia, 2004; Martin Andres, Tapia Garcia, & Del Moral Avilia, 2005) corrections, but in all considered settings the correction was very close to 0, thus the resulting approach performed similarly to the uncorrected methods and therefore, the results are not presented here.…”

“…Continuity-corrected methods for interval estimation were widely discussed with respect to binomial outcomes (Yates, 1934; Adler, 1951; Pirie & Hamdan, 1972; Schouten, Molenaar, van Strike, & Boomsma, 1980; Upton, 1982; Hauck & Anderson, 1986; Haviland, 1990; Martin Andres & Tapia Garcia, 2004; Martin Andres, Tapia Garcia, & Del Moral Avila, 2005; Soulakova & Bright, 2013). The most commonly used approaches incorporate the Yates continuity correction (Yates, 1934; Adler, 1951; Upton, 1982; Hauck & Anderson, 1986; Haviland, 1990), denoted by c Y , Schouten-Molenaar-van Strik-Boomsma correction (Schouten et al, 1980), denoted by c S , and Hauck-Anderson correction (Hauck & Anderson, 1986), denoted by c HA .…”

“…In addition, the correction based on methods by Pirie and Hamdan (1972), Martin Andres and Tapia Garcia (2004), and Martin Andres et al (2005) was addressed for binomial settings (Soulakova & Bright, 2013). The latter correction is very close to zero for large time intervals (or large sample sizes in the one-unit scenario) and thus is not discussed in this paper.…”