We show that bosonic correlations from quantum states with a well-behaved (positive) Glauber–Sudarshan~$P$ distribution—which include coherent states, thermal states and all the states that can be deemed classical—are a manifestation of Simpson’s paradox: they are spurious correlations from statistical (ensemble) averages over uncorrelated measurements made in varying geometries, with symmetry breaking as the confounding factor. Bosonic correlations encoded by the wavefunction appear to be formed in the geometry of the statistical ensemble, whereas the measurements are actually made in a different geometry, which varies from realization to realization of the experiment. The statistical average restores the symmetry and correlates the bosons. This cogent explanation calls to distinguish between quantum and statistical averages.