Fundamental Measurement of Rank-Ordered Objects

A Rasch measurement model can be constructed to meet the requirements of rank ordered data. If multiple rankings of the same objects are available, then the parameters of the objects can be estimated, along with their standard errors and also with statistics summarizing the fit of the data to the measurement model. This paper summarizes the relevant theoretical principles associated with rank ordering and presents an example of this sort of analysis. The example includes H. Polskin's (1988) rankings of seven play-by-play baseball announcers on six specific items of performance. The application of the principles of fundamental measurement to rank ordered data provides the means to convert entirely local rankings into generalizable measures of the latent abilities. Moreover, fit statistics for each object and for each ordering enable a determination of the success of the ranking process as a measurement operation. (TJH)