Construction of Balanced Incomplete Block Designs within Unequal Block Sizes

Abstract

-. "Since. statisticians do not usually perform an experiment, their claim to attention when they write on experimentation requires some explanations", William Cochran and Gertrude Cox (1957). Block designs are widely used in many fields of research. Their most common type is the randomized (complete) block design. It is not applicable in all circumstances. If the numbers of (elements are too large to preserve homogeneous conditions within complete blocks or the sizes of blocks are determined by the nature of the experimental material, then incomplete block designs arc used. A wide range of these designs is available for planning experiments in blocks of equal sizes but with a smaller number of plots than the total number of treatments. An experimenter who wants all the contrasts between treatment lo bc confounded with blocks to the same extent may use a balanced incomplete block design (RIBD). Ilcsigns of that type can be constructed for any number of equally replicated treatments and any size of equal blocks but may require quite a large number of replicates. If the experimenter is willing to accept that some of the possible treatment contrasts are more confounded than others, he may choose one of the various partially balanced incomplete block (PBIR) designs listed in standard works on experimental design, ('Cochran and Cox (1957). These designs require an sm