Response to Eisenstein and Bunn's Null Hypothesis Comment on Cosmological Birefringence

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.