Theq-mutator theory is used to connect the value of1−|q|,the parameter measuring the “difference” between quons and ordinary bosons and fermions, to experiments that test the spin-statistics connection. Such calculations are best carried out using a density matrix formulation because a superselection rule prevents transitions between states associated with different representations of the permutation group. The interpretation of the experimental results, however, in terms of a quantitative limit on1−|q|can be easily misled by the density matrix formulation. As a concrete example, the theory is applied to a spin-statistics test for photons. The formalism is then applied to spin-statistics tests for electrons in atomic helium and for16Onuclei in molecules. Finally, the analysis is used to extend experimental limits on composite systems such as16Onuclei to provide a test of the spin-statistics connection for the constituents of those composite systems (nucleons and quarks in the case of oxygen nuclei). ©2000 American Institute of Physics.