Degrees of freedom effect

Tin, Y.N. Rabinovitch, B.S. Degrees of Freedom Effect and Internal Energy Partitioning Upon Ion Decomposition. J. Phys. Chem. 1970, 74, 1769-1775. 

Bente III., P.F. McTafferty, F.W. McAdoo, D.J. Tifshitz, C. Internal Energy of Product Ions Formed in Mass Spectral Reactions. The Degrees of Freedom Effect. J. Phys. Chem. 1975, 79, 713-721. 

In total we have 16x4=64 degrees of freedom. If we remain with the basic form of model (21.8) then we could, for example, simply treat the data as 16 replicated measurements on each of four doses and lit a common intercept a and common slope jS. This is model A of Table 21.1 and has two model degrees of freedom, leaving 62 error degrees of freedom. Because we have made no attempt to incorporate the information that measurements are made repeatedly on the same subjects, all of the variation between subjects must be contained in these 62 degrees of freedom. Effectively we have the sort of analysis which would be appropriate for a trial in which 64 subjects were split at random into four different doses. If we make a minimal attempt to recognize that four data values are provided by every subject and fit a model with a different intercept for each patient but a common slope, we then have model B. In model C, a quadratic parameter, y, is fitted as well as a cubic parameter, 8, so that the model is of the form... 

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