A measure is introduced of the information provided by an experiment. The measure is derived from the work of Shannon  and involves the knowledge prior to performing the experiment, expressed through a prior probability distribution over the parameter space. The measure is used to compare some pairs of experiments without reference to prior distributions; this method of comparison is contrasted with the methods discussed by Blackwell. Finally, the measure is applied to provide a solution to some problems of experimental design, where the object of experimentation is not to reach decisions but rather to gain knowledge about the world.
D. V. Lindley. "On a Measure of the Information Provided by an Experiment." Ann. Math. Statist. 27 (4) 986 - 1005, December, 1956. https://doi.org/10.1214/aoms/1177728069