  The microscopic wave functions of the composite fermion theory can
incorporate electron mass anisotropy by a trivial rescaling of the coordinates.
These wave functions are very likely adiabatically connected to the actual wave
functions of the anisotropic fractional quantum Hall states. We show in this
article that they possess the nice property that their energies can be
analytically related to the previously calculated energies for the isotropic
states through a universal scale factor, thus allowing an estimation of several
observables in the thermodynamic limit for all fractional quantum Hall states.
The rather weak dependence of the scale factor on the anisotropy provides
insight into why fractional quantum Hall effect and composite fermions are
quite robust to electron mass anisotropy. We discuss how better, though still
approximate, wave functions can be obtained by introducing a variational
parameter, following Haldane [Phys. Rev. Lett. {\bf 107}, 116801 (2011)], but
the resulting wave functions are not readily amenable to calculations. Our
considerations are also applicable, with minimal modification, to the case
where the dielectric function of the background material is anisotropic.
