Let's say we have a RxC contingency table, with R=C. How could one best repopulate the table such that:
- all counts reside in the off-diagonal cells (zero's on the diagonal);
- marginal frequencies remain the same;
- the value of Chi square is maximal.
I can imagine a very 'exhaustive' approach by calculating the Chi square for each possible repopulation and taking the table that produces the highest Chi square value, but there has to be an elegant much better way to solve this! A formal proof may be difficult, but a smart algorithm should exist.