Abstract A quantitative measure of the validity of the MWC description of cooperative binding equilibria has been obtained which uses only the Adair constants. This is accomplished through simple relationships using the zeros of the Adair binding polynomial and unique properties of the zeros of MWC polynomials as described in the accompanying paper (W.E. Briggs, Biophys. Chem. 24 (1986) 311). The method is applied to oxygen binding to a large number of hemoglobins under a wide variety of conditions. In most cases, exemplified by human hemoglobin under a wide range of conditions, the MWC model is allowed and the probability of its suitability is determined. The probability given by this method correlates directly with the deviation between the experimental binding curve and that derived from the theory. In several cases the pattern of the Adair polynomial zeros immediately excludes the MWC model, most notably for carp hemoglobins. A physical picture of cooperative binding site interactions is nevertheless obtained from the patterns of zeros as they relate to the factorization of the binding polynomial.