By a study of the duality relationships of a large number of balanced and partially balanced incomplete block designs, certain ones have been found which lend themselves nicely to interblock analysis. Besides facilitating this analysis, these designs make possible the use of a new method for studying the relative variability of the inter and intra-block error. These "nice" designs, which are called twice balanced, have the property that their duals are also balanced or partially balanced. In the partially balanced designs, the investigation has been confined to those with two associate classes. Some methods are shown which may be used to prove that a dual is twice balanced. The twice balanced designs which have been found are catalogued, showing the plan numbers of the design and the dual,and the necessary identifying parameters or both. The proofs used in verifying the designs to be twice balanced are also indicated. Finally, there is an illustrative example making use of the methods and tables introduced in this paper. It includes a new computing method to be used for finding estimates of the treatment effects in a mixed model experiment. / Master of Science