Abstract: | Let X 1, X 2, ... be a sequence of i.i.d. random variables, X i∼ F θ, θ∈Θ. Let N 1 and N 2 be two stopping rules. For a class of exponential families { F θ: θ∈Θ} we show that the experiment Y 1 = ( X 1, ..., X N1) carries more statistical information than Y 2 = ( X 1, ..., x N2) only if N 1 is stochastically larger then N 2 |