On the number of contingency tables and the independence heuristic. Issue 1 (28th February 2022) - Lyu, Hanbaek; Pak, Igor
Abstract: We obtain sharp asymptotic estimates on the number of n × n n × n contingency tables with two linear margins C n Cn and B C n BCn . The results imply a second‐order phase transition on the number of such contingency tables, with a critical value at B c : = 1 + 1 + 1 / C B_c:=1 + 1+1/C . As a consequence, for B > B c B>B_c, we prove that the classical independence heuristic leads to a large undercounting.