  We extend the notion of test module filtration introduced by Blickle for
Cartier modules. We then show that this naturally defines a filtration on unit
$F$-modules and prove that this filtration coincides with the notion of
$V$-filtration introduced by Stadnik in the cases where he proved existence of
his filtration. We also show that these filtrations do not coincide in general.
Moreover, we show that for a smooth morphism $f: X \to Y$ test modules are
preserved under $f^!$. We also give examples to show that this is not the case
if $f$ is finite flat and tamely ramified along a smooth divisor.
