: One of the main basis in experiment of design is reducing experiment error. block designs often serve this purpose. If there are two flexible sources of confusion, then the omission of these two sources is possible only through blocking in two directions. In other word, two blocking factors are used with one factor representing the rows of the design and the other factor representing columns. This kind of design is called row – column design. For instance, in a agricultural experiment the rows and columns of a design might be used to control field gradient and soli type respectively. Row – column designs with p rows and q columns include pq plots. More generally, an experiment may involve groups of row – column designs each with pq plots. These groups may represent a further blocking factor or provide repeats of the basic experimental design. For example, the agricultural experiment mentioned above may be carried out at a number of different location. Such designs have ? treatments in b blocks of size pq, in a way that treatments within each block set out in a row – column design consist of p rows and q columns. Since the rows and the columns are nested within blocks, these designs are called nested row – column designs (NRC). In chapter two, intra – block and inter – block analysis are examined and moreover, It also introduces criteria of universal optimality and several criteria of special optimality. In order to construct row – column designs treatments can be devoted to ? treatment combinations using pseudo factors. Then, by double confounding method, a row – column design is constructed. In chapter three factorial designs are described briefly and a method for confounding in row – column designs has been expressed
