ABSTRACT
In this chapter, the authors deal with notation and statistical models, and provide relevant study designs and sampling distributions. Ordered r×2 $ r\times 2 $ tables may occur when the authors simply have constraints that imply an ordering of the probabilities of the outcome of interest—usually called success—over the r groups. In that case, a trend means that the grouping is consistent with an ordering from the lowest to the highest probability of success, or the other way around, from the highest to the lowest probability of success. Testing for unspecific ordering—also called testing for ordered alternatives—was proposed by Bartholomew and described in the seminal textbook by Barlow et al. Testing for linear trend has a long history, as it goes back to Cochran and Armitage. They proposed a test for trend in the linear model and estimated the trend by the standard linear regression coefficient.
