  We consider parametric hypotheses testing for multidimensional ergodic
diffusion processes observed at discrete time. We propose a family of test
statistics, related to the so called $\phi$-divergence measures. By taking into
account the quasi-likelihood approach developed for studying the stochastic
differential equations, it is proved that the tests in this family are all
asymptotically distribution free. In other words, our test statistics weakly
converge to the chi squared distribution. Furthermore, our test statistic is
compared with the quasi likelihood ratio test. In the case of contiguous
alternatives, it is also possible to study in detail the power function of the
tests.
  Although all the tests in this family are asymptotically equivalent, we show
by Monte Carlo analysis that, in the small sample case, the performance of the
test strictly depends on the choice of the function $\phi$. Furthermore, in
this framework, the simulations show that there are not uniformly most powerful
tests.
