There is one distinction which must be clearly made, but is usually treated in an ambiguous fashion. This is the difference between the two choices to be made. First the function which describes the difference between the observations and the predictions of the model. The second is the choice of the method by which this function will be minimized.
There are several methods of minimization commonly used today. Most are described in detail below. Each of them can be used to minimize any function.
In crystallography three functions commonly used. They are the least-squares residual, the empirical energy function, and the correlation coefficient.
The least-squares residual function is
where 
and 
are the value and standard deviation
for observation
number i. 
is the model's prediction for observation i using
the set of model parameters 
. The values of the parameters found by
minimizing this function are those which have the smallest individual
standard deviation, or the smallest probable error[4].
The justification for refining against an empirical energy function is the belief that the true protein structure should be at an energy minimum as well as a best fit to the crystallographic observations. While this is undoubtedly correct in the absence of errors in the measured intensities and energy parameters, an analysis of the effect of the presence of such errors has not been done. In practice, usually the parameters of the energy function are chosen in a fashion to allow the energy to mimic the least-squares residual. Confusion can result if the value of such an ``energy'' function is interpreted as an energy.
The correlation coefficient is a different measure of the agreement between the model and the observations. In statistics it is used to judge whether there is any agreement at all. This makes it very sensitive to changes in the model when the agreement between the model and the observations is only barely detectable. The correlation coefficient is commonly used in the solution of rotation functions, but has not been used commonly in individual atom refinement.
To describe a refinement protocol it is not sufficient to state one or the other of these choices. One can not meaningfully state that a model was refined with ``least-squares''. Both the function and the method must be stated.