  In special relativity, testing for spatial anisotropy usually means testing
for anisotropic propagation of light. This paper explores a different
possibility, in which light is still assumed to propagate isotropically in all
frames with an invariant speed, yet other physical effects exhibit a direction
dependence. If spatial isotropy is not assumed in the derivation of the
coordinates transformations, the resulting equations differ from the Lorentz
relations by an additional factor $(\dfrac{c - v}{c + v})^{\kappa}$, where
$\kappa$ is the anisotropy exponent, which depends on the direction chosen as
the x-axis. Time dilation and length contractions become direction dependent.
The anisotropy exponent is frame-independent, so no preferred isotropic frame
exists if $\kappa$ is non-vanishing. The Doppler shift can be used to measure
this exponent and determine experimentally the degree of anisotropy our
universe actually possesses.
