β Scribed by William V. Gehrlein; Peter C. Fishburn
No coin nor oath required. For personal study only.
Measurement in the social sciences often involves an attempt to completely order a set of entities on the basis of an underlying attribute. However, limitations of the measurement process often prevent complete empirical determination of the desired ordering. Nevertheless, the ordinal data obtained from the measurement process can be used in attempting to recover or construct more of the underlying order than is provided by the data. Previous research has shown that a simple one-stage construction method, referred to as the 'cardinal rule', is fairly effective in correctly identifying ordered pairs in the underlying linear order that axe not identified by the measurement process. The present paper re-examines the cardinal rule from the perspective of construction methods based on simple counting measures derived from the data, and argues that it is the best one-stage method in this class when a natural monotonicity assumption holds for the measurement process. The paper then examines twostage construction rules that are based on the cardinal rule and the simple counting measures. It is shown that one of the two-stage rules gives better overall results than does the cardinal rule by itself.
π SIMILAR VOLUMES
The graphical method and the iterative method for analysing kinetic data for metal speciation in waters are described. The graphical method involves successive subtractions of one component from the total concentration of the metal remaining, beginning with the slowest component. The iterative metho