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Motivated by applications to perverse sheaves, we study combinatorics of twocell decompositions of the symmetric product of the complex line, refining thecomplex stratification by multiplicities. Contingency matrices, appearing inclassical statistics, parametrize the cells of one such decomposition, whichhas the property of being quasi-regular. The other, more economical,decomposition, goes back to the work of Fox-Neuwirth and Fuchs on thecohomology of braid groups. We give a criterion for a sheaf constructible withrespect to the ''contingency decomposition'' to be constructible with respectto the complex stratification. We also study a polyhedral ball which we callthe stochastihedron and whose boundary is dual to the two-sided Coxeter complex(for the root system $A_n$) introduced by T.K. Petersen. The Appendix by P.Etingof studies enumerative aspects of contingency matrices. In particular, itis proved that the ''meta-matrix'' formed by the numbers of contingencymatrices of various sizes, is totally positive.

Contingency Tables with Variable Margins (with an Appendix by Pavel Etingof)