Since the seminal work of Teece et al. (1994) firm diversification has been found to be a non-random process. The hidden deterministic nature of the diversification patterns is usually detected comparing expected (under a null hypothesys) and actual values of some statistics. Nevertheless the sta… ndard approach presents two big drawbacks, leaving unanswered several issues. First, using the observed value of a statistics provides noisy and nonhomogeneous estimates and second, the expected values are computed in a specific and privileged null hypothesis that implies spurious random effects. We show that using Monte Carlo p-scores as measure of relatedness provides cleaner and homogeneous estimates. Using the NBER database on corporate patents we investigate the effect of assuming different null hypotheses, from the less unconstrained to the fully constrained, revealing that new features in firm diversification patterns can be catched if random artifacts are ruled out.