Existing evidence on the origin times of magnitude earthquakes worldwide, based on authoritative earthquake catalogs, does not permit rejection of the null hypotheses of random coincidental occurrence at any time during the Earth or the Moon cycles. Specifically, the nonparametric Kuiper test statistics for cyclic variations applied to seismic evidence resulting from the empirical distributions of the earthquake origin time Julian day (JD) and the Moon phase (MP) do not allow the rejection of the null hypotheses of uniform distributions within the corresponding cycles. On the other hand, the same Kuiper test permits the rejection of the null hypotheses of the same chance of occurrence on any JD or MP for strong magnitude earthquakes, at least for the past four decades of presumably the best‐earthquake determinations and, in particular, for earthquakes in the Northern Hemisphere (with an evident seasonal pattern). The nonparametric two‐sample Kolmogorov–Smirnov test statistics suggest no preferred distances to the Moon at the occurrence of large earthquakes. All of this contributes, to the results of solid statistical testing of hypotheses, for a better understanding of the complex seismic response of the Earth’s lithosphere to periodic gravitational loading.