The relation between an extreme proportion and a less extreme proportion, in the context of the comparability of tests

Data are sometimes encountered consisting of the proportions of items falling into each of three ordered categories in a number of different circumstances. The examples in this paper concern properties of particulate material, such as the proportion of particles considered to be fractured. Methods are proposed for relating the proportion satisfying some stringent criterion (e.g., two or more fractured faces) to the proportion satisfying some less stringent criterion (e.g., one or more fractured faces). Emphasis is on methods whose success or otherwise can be seen graphically.