A Screening Analysis for Incomplete Ranking Data

Abstract

We consider the setting where a group of n judges are to rank independently a series of k objects. When all judges rank all treatments, this coincides with the no-interaction two-way lay-out setting with one observation per cell. However, many times the intended complete rankings are not realized and we are faced with analysing randomly incomplete rank vectors. We propose a new screening approach to analysing such data realizations. For discussion, we concentrate on the problem of testing for no differences in the objects being ranked (i.e. they are indistinguishable) against general alternatives, but our approach will also be quite appropriate for restricted (e.g. ordered or umbrella) alternatives. We detail the algorithm for computation of the relevant Friedman-type statistic in the general alternatives setting and present the results of a simulation study to assess the effectiveness of the algorithm.