Various workers have shown that considerable economies in experimentation can be achieved by the use of identical twins, halves of leaves and halves of plants. The basic statistical principle enabling these economies is that of incomplete block designs. These make possible the comparison of treatments within pairs of identical twins, pairs of half-leaves or whatever grouping is used, so that experimental error arises only because of differences between individuals within the pairs.

Extensive use of these natural groupings is possible only when the possible incomplete block designs have been enumerated. The purpose of this bulletin is to present what is essentially a complete array of incomplete block designs with blocks of two plots.

The balanced incomplete block design requires (n-1) replications, where n is the number of treatments. Any design using a lesser number of replications must necessarily be unbalanced. Designs are presented which require (n-2), (n-3), ... , three replications, whenever such is possible, for any number of treatments between 6 and 12.

These designs have been extracted from a pool of designs formed by (a) the class of partially balanced incomplete block designs with two classes of associates and (b) the class of circulant designs. The design chosen to cover each situation is the design which has the highest efficiency factor among all the designs in the pool applicable to the given situation.

The tabulation of material necessary for the analysis of the respective designs is made to facilitate computations.

The computations are exemplified by the inclusion of a worked example covering both the intrablock and interblock analysis.