We know that the best linear combination of the intra- and inter-block estimates is Intra-estimatexInter-variance+Inter-estimatexIntra-variance / Intra-variance + Inter-variance ; however, this combined estimate is merely theoretical, since we do not know in practice the exact inter- and intra-variances. A reasonable solution is to use a random weight which can be computed from the data of our experiment, but so far there has been no practical solution without severe restrictions on the size of the experiment, and no solution at all for a clear answer to the question of how much we recovered. In fact, the experimenter applying the methodology available to him now, cannot be sure that he is really improving the accuracy of his estimation. This research has achieved the following: 1. A new method of combining two independent estimates has been developed. This method has its use in incomplete block designs, in similar experiments, and in randomized block designs with heterogeneous variances. The improvement introduced by this method is very satisfactory, compared with the utmost possible theoretical improvement. 2. A procedure for recovering the inter-block information in B.I.B. designs was given, which is applicable in experiments as small as t = 4. 3. It has been proven that the practical utilization of inter-block information is possible in any P.B.I.B. with seven treatments or more. 4. A general procedure for recovering the inter-block information in P.B.I.B.'s with two associate classes was given. 5. An inter-block analysis of singular and semi-regular group divisible designs was discussed, which makes a partial utilization of the inter-information possible. In general, this work has two merits: 1. It makes possible the utilization of the interblock information in small and moderate size experiments. 2. As a ratio of the utmost possible theoretical recovery (by combining linearly), either exactly or a lower bound of the ratio of recovery is always computable. Tables which enable the experimenter to use the procedures described in this dissertation were given. The ratios of recovery listed in these tables show that the new method gives good results where the old method is not applicable, and when the old method starts, hopefully, to be valid, the ratio of recovery achieved by the new method starts to approach the theoretical value that can be achieved, assuming the intra- and inter-variance are known. / Ph. D.