Regardless of the outcome of the test, the classical researcher does not use the test of hypothesis to respecify the model and reestimate from the same data. I error is almost always somewhat arbitrarily chosen by the researcher. It is the choice of these two probabilities that determines the loss that the researcher is willing to incur in making an incorrect decision. The situation may be pictured as in figure x.x. The family of concave curves is a set of indifference curves showing the trade-off that the researcher is willing to make between the two types of errors.
Utility increases as one moves closer to the origin.
If a model is to be chosen in a mechanistic fashion then the loss function should be clearly stated at the outset. One way to do this is to choose the model which is most informative about the data. An information criterion permits the researcher to choose a model under the double consideration of accuracy of estimation and best approximation to reality. That is, observing the proposed model tells us something about the unknown model. It is a decrasing function.