Molecules with isolated compound state resonances decompose with state specific unimolecular rate constants. In some cases, this state specificity can also be identified as mode specific decomposition. Mode specificity means there are exceptionally large or small state specific rate constants depending on which internal modes are excited in forming the resonance state. The ability to establish the modes excited requires that the energies, for resonance states yielding mode specific behavior, can be predicted by finding patterns in the positions of these states in the spectrum. Such patterns allow a zero-order Hamiltonian and basis set to be used to assign quantum numbers to the resonances and to define the type of mode specificity. A situation contrary to one where all the resonance states exhibit mode specificity is statistical state specificity. For this case there are no patterns in the positions of the resonances in the spectrum, so that all the resonance states are intrinsically unassignable. Small and large fluctuations of the state specific rate constants are simply random occurrences, and cannot be associated with any pattern. Statistical inaccuracies make it difficult to identify mode specificity from a distribution of nearest neighbor energy levels. For all types of state specificity (including mode specificity and statistical state specificity), a microcanonical ensemble of compound state resonances will usually not decay exponentially. However, a corresponding result is often not obtained by classical mechanical simulations. The nonexponential decay of a microcanonical ensemble of resonance states results in monoenergetic chemical activation and thermal Lindemann-Hinshelwood rate constants which deviate from those of RRKM theory.