  The distribution of arrival directions of ultra-high energy cosmic rays may
yield clues to their mysterious origin. We introduce a method of {\it invariant
statistics} to analyze cosmic ray data which eliminates coordinate-dependent
artifacts. When combined with maximum likelihood analysis, the method is
capable of quantifying deviations of the distribution from isotropy with high
reliability. We test our method against published AGASA events with energies
above $4 \times 10^{19}$ eV. Angular cuts from observational limitations are
taken into account. A model based on the Fisher distribution reveals the
rotation of the Earth with the axis $\hat n$ along the direction ($5^h 53.36^m,
85.78^{\circ}$) in $(RA,DEC)$ coordinates, which is within $5^{\circ}$ of the
equatorial north pole. Global anisotropy of the data, if any, hinges on finer
understanding of detector acceptance than what is available from the published
literature.
