THE RECOVERY OF INTER‐BLOCK INFORMATION IN BALANCED INCOMPLETE BLOCK DESIGNS

Abstract

Incomplete block and quasi-factorial designs of various kinds were first introduced by the author a few years ago. All these designs have the property that the number of varieties (or treatments) included in each block is smaller than the total number to be tested. There is consequently a gain in precision due to the use of smaller blocks, at the expense of loss of information on those varietal comparisons which are confounded with blocks. In the original papers only the complete elimination of inter-block differences was considered. These inter-block comparisons will, however, contain an appreciable amount of information, amounting in the limiting case, when the inter-block and intra-block comparisons are of equal accuracy, to a fraction 1-E of the total information, where E is the efficiency factor.