  We generalize results of Mingo and Nica on graded independence from the
context of $\mathbb Z_2$--graded (Fermionic) noncommutative probability spaces
to that of $\mathbb Z_n$--graded noncommutative probability spaces. We show
that for $q$ a primitive $n$-th root of unity, the $q$-cumulants defined by
Nica linearize the addition of homogeneous $\mathbb Z_n$--graded independent
random variables.
