The previous two lessons both describe data reduction principles in the following way. A function *T*(**x**) of the sample is specified, and the principle states that if **x** and **y** are two sample points with *T*(**x**) = *T*(*y*), then the same inference about *θ* should be made whether *x* or *y* is observed. The function *T*(*x*) is a sufficient statistic when the Sufficiency Principle is used. The "value" of *T*(*x*) is the set of all likelihood functions proportions to *L*(*θ*|**x**) if the Likelihood Principle is used. The Equivariance Principle describes a data reduction technique in s slightly different way. In any application of the Equivariance Principle, a function *T*(**x**) is specified, but if *T*(**x**) = *T*(**y**), then the Equivariance Principle states that the inference made if **x** is observed should have a certain relationship to the inference made if **y** is observed, although the two inferences may not be the same. This restriction on the inference procedure sometimes leads to a simpler analysis, just as do the data reduction principles discussed in earlier lessons.