We provide some statistics about an irreducibility/reducibility test for multivariate polynomials over finite fields based on counting points. The test works best for polynomials in a large number of variables and can also be applied to black-box polynomials.
"A Quick and Dirty Irreducibility Test for Multivariate Polynomials over $\Bbb F_q$." Experiment. Math. 14 (4) 415 - 422, 2005.