  Eisenstein and Bunn have widely circulated a Comment (astro-ph/9704247)
suggesting a non-standard null hypothesis in a test for cosmological
birefringence. The Comment misrepresents the procedure used by Nodland and
Ralston (B. Nodland and J. P. Ralston, Phys. Rev. Lett. 78, 3043 (1997);
astro-ph/9704196) and lacks statistical basis; no calculations were reported,
but sweeping conclusions were drawn from eyeballing a single scatter plot. The
results of the suggested procedure range from an underestimate of the
statistical significance of well-correlated data, to a failure of detecting a
perfect correlation in the limit of strong cuts. We verified these faults by
performing the actual calculation which EB suggested, but neglected to carry
out themselves. Furthermore, the calculation showed that the original
correlation remains statistically significant, with the lego-plot of 1/P versus
s showing a persistent bump, and the anisotropy direction s remaining in the
same direction as previously reported.
