Alicja Ciok

Generating random MxK tables when row and column totals and cell ranges are given

844

Abstract

The paper concerns generation of two-way random tables suitable for performing conditional exact tests of independence provided that row and column totals and cell ranges are fixed. It is argued in the Introduction that tables with fixed cell ranges are common in psychology, sociology or marketing science and therefore conditional exact tests of this kind are needed in practice. The proposed generation modifies the Patefield's algorithm which is appropriate when only row and column totals are fixed. The distributions used in the Patefield's algorithm to generate cell values are restricted to the given range successively for all cells except those in the last row and column. This is followed by an iterative displacement of masses among suitably chosen cells until either all requirements are satisfied or the generated table is rejected as impossible to correct. Efficiency of the whole procedure is tested on a set of examples and is shown to be much better than that of hypothetical procedure which generates tables by a straightforward application of Patefield's distributions restricted to the fixed range and which rejects non-admissible tables. The influence of iterative displacements on sets of generated tables is discussed.

Key words: conditional exact test, independence, computational feasibility, simulation-and-reject procedure.