5 factors: 16 combinations
 (00000,00011,00101.001 0,01001,01010,01100,01111,
 10001,10010,10100,10111,11000,11011,11101,11110)
 5 factors: 8 combinations
 (00000,00110,01011,01101,10011,10101,11000,11110).

 Suppose it is decided that a particular number of combinations are to be used and, further, that the
 presentation purposes both the combination of the lower level for all factors and the combination of the
 upper levels of all factors are to be included (note that this will not normally be statistically beneficial. The
 principles for choosing the other combinations are
 (1) the two levels of each factor should be nearly equally represented,
 (2) the four combinations of levels for each pair of factors should be equally represented,
 (3) to remember the ideal properties of the "nice" fractions in maximising information about main effects.

 Many practical situations using subsets of factorial structures require two-level factors and the logic of
 selecting appropriate subsets is clearer for two levels per factor. Nevertheless it is possible to select subsets
 from three- or four- level factors using the same principles. Thus, suppose we require twelve combinations
 from a 2x3x4 structure. A suitable set would be

 (000,101,102,003,110,011,012,113,120,021,022,123)

 which includes all the 2x3 combinations twice, all the 3x4 combinations once and the 2x4 combinations
 each once or twice.

 5.4 An Example

 To consider further the arguments pertinent to the choice of experimental treatments for type 3 structures
 we shall use an example of a verification trial from Ipiales (Woolley et al. 1988). The experiment was for a
 beans/maize intercropping mixture and the actual treatments used were


 Variety Density Seed
 Beans Maize Beans Maize Fertiliser Treatment

 1) 1 A 8 16 100
 2) 1 A 8 16 100
 3) 2 A 12 16 100
 4) 2 A 16 16 100
 5) 3 A 16 16 100
 6) 2 A 16 16 300
 7) 2 B 16 16 300
 8) 2 A 16 16 300 Yes


 The treatments were designed in a step-wise fashion to assess the effects of a sequence of changes,
 depending on (a) the size of the effects detected in previous trials and (b) the expected adoption sequence
 by farmers. Treatment 1 was intended to be the individual farmer's practice in contrast to treatment 2
 which was the to be the average practice of the group; in fact they emerged as virtually identical. Treatment
 3 introduced an improved bean variety. Treatment 4 changed the proportion of beans/maize. Treatment 5
 introduced a possible alternative, earlier,bean variety which might take better advantage of the increased
proportion of beans. Treatment 6 added more fertilizer to treatment 4. For treatment an alternative maize
variety (at the higher fertilizer level) was tried. Finally(treatment 8) a seed treatment was added to
treatment 6. The logic of the stepwise evolution of treatments is simple and easily understood. In statistical
terms it is also, unfortunately, inefficient in the use of resources. Each question which the treatments were