EQUINEIGHBOURED XPERIMENTAL DESIGNS

This paper introduces a new class of designs called equi-neighboured designs. An equineighboured design has the property that every unordered pair of treatments occurs as nearest neighbours equally frequently at every level. These designs are defined in Section 4 and shown to be balanced when neighbouring observations are correlated. Some equineighboured designs are constructed using a complete set of orthogonal Latin squares. Cyclic equineighboured designs are also defined.     

Resolvable row–column designs

This paper discusses resolvable row-column designs for v treatments arranged in b blocks each comprising pq units further grouped into p rows and q columns. A resolvable row-column design has v =pqs treatments set out in r groups of s blocks. Each rectangular block has p rows and q columns.     

PARTIALLY EQUINEIGHBOURED DESIGNS

This paper presents further results on a class of designs called equineighboured designs, ED. These designs are intended for field and related experiments, especially whenever there is evidence that observations in the same block are correlated. An ED has the property that every unordered pair of treatments occurs as nearest neighbours equally frequently at each level. Ipinyomi (1986) has defined and shown that ED are balanced designs when neighbouring observations are correlated. He has also presented ED as a continuation of the development of optimal block designs. An ED would often require many times the number of experimental materials needed for the construction of an ordinary balanced incomplete block, BIB, design for the same number of treatments and block sizes. Thus for a relatively large number of treatments and block sizes the required minimum number of blocks may be excessively large for practical use of ED. In this paper we shall define and examine partially equineighboured designs with n concurrences, PED (n), as alternatives where ED are practically unachievable. Particular attention will be given to designs with smaller numbers of blocks and for which only as little balance as possible may be lost.