All three theories model the temperature dependence of k using an equation of the form
for some constant C, where α = 0, , and 1 give Arrhenius theory, collision theory, and transition state theory, respectively, although the imprecise notion of ΔE, the energy needed to overcome the activation barrier, has a slightly different meaning in each theory.  In practice, experimental data does not generally allow a determination to be made as to which is "correct" in terms of best fit.  Hence, it must be remembered that all three are conceptual frameworks that make numerous assumptions, both realistic and unrealistic, in their derivations.  As a result, they are capable of providing different insights into a system.