2.6 Factorial Structure in an Unreplicated Trial


 This trial at Poza Rica Station is described as an unreplicated observation trial and I have not seen the
 location of the trial. However since there are 36 treatment combinations I would question why it was not
 designed as an experiment. With 36 treatment combinations it is by no means clear that direct replication is
 necessary since hidden replication may be sufficient.

 The 36 treatment combinations are

 6 herbicides x 2 cover crops x 3 planting dates.

 Assume that we are interested in main effects and in the combined effects of each pair of factors. The 36
 plots should probably be grouped in six blocks of six plots per block, though detailed examination of the
 site might suggest alternative blocking patterns. In deciding the allocation of treatment combinations to
 blocks we would try to arrange

 (i) all six herbicides (h) in each block,
 (ii) both cover crops (c) to occur three times in each block,
 (iii) each planting date (d) to occur twice in each block,
 (iv) all six combinations of cover crop x planting date to occur in each block.

 Other requirements for equal occurrence of combinations of pairs of factors in each block are impossible in
 blocks of six plots (Using three blocks of twelve plots would allow all combinations of herbicide x cover
 crop in each block). The design for six-plot blocks is constructed by allocating the six cover crop x planting
 dates to each block and then distributing the herbicide treatments so that no herbicide level is repeated in a
 block.


 Block 1 Block 2 Block 3 Block 4 Block 5 Block 6


 clplhl clplh2 clplh3 clplh4 clplh5 clplh6
 clp2h2 clp2h4 clp2h6 clp2h3 clp2hl clp2h5
 clp3h3 clp3h5 clp3hl clp3h2 clp3h6 clp3h4
 c2plh4 c2plh3 c2plh5 c2plh6 c2plh2 c2plhl
 c2p2h5 c2p2h6 c2p2h4 c2p2hl c2p2h3 c2p2h2
 c2p3h6 c2p3hl c2p3h2 c2p3h5 c2p3h4 c2p3h3


 (The choice for the allocation of herbicides to block,c,p combinations is very wide and is equivalent to a
Latin Square solution.)