Random design

Figure 5. Randomly designed training set employing uniform distribution.

There is nothing that says we must slavishly follow one of the structured or random experimental designs. For example, we might wish to combine the features of structured and random designs. Also, there are times when we have... 

Kamman NC, Lorey PM, Driscoll CT, Estabrook R, Major A, Pientka B, Glassford E. 2003. Assessment of mercury in waters, sediments, and biota of New Hampshire and Vermont lakes, USA, sampled using a geographically randomized design. Environ Toxicol Chem 23 1172-1186. 

A number of medium- to long-term enviromnental monitoring networks and programs have been developed over the past 4 decades in the United States, all of which have had to deal with network design issues noted here. Some of these efforts are summarized in Table 5.3. As indicated in Table 5.3, some programs have emphasized random or partially random designs, whereas others have utilized nonrandom designs but based on specific site criteria. 

Soybean bloassays of root exudates. Four soybean seeds ( Bragg ) were planted In each of 100 12.5 cm plastic pots filled with an artificial soil mix consisting of perlite/coarse sand/coarse vermiculite 3/2/1 by volume. After one week the plants were thinned to two per pot and the treatments were begun. The experimental design was a completely randomized design with 10 replications (pots) per treatment. On the first day of each week each pot was watered with 300 ml effluent from the appropriate growth units. On the fifth day of each week all pots were watered with Peter s Hydro-sol solution with CaCNOj. At other times the pots were watered as needed with tap water. On the second and fifth day of each week the height of the soybeans (base to apical bud) was measured. 

Root elongation bloassay of root exudates. Five ml aliquots of the root exudates were pipetted onto three layers of Anchor1 germination paper In a 10 by 10 by 1.5 cm plastic petri dish. Twenty five radish or tomato seeds were placed in a 5x5 array in each petri dish. Radish seeds were incubated at 20C for 96 hours tomato seeds were incubated at 20C for 168 hours, before the root length was measured. Experimental design was a completely randomized design with three replications (dishes) per treatment per bioassay seed species. The bioassay was repeated each week for 23 weeks. 

Nevertheless, it is wise to examine the randomized design to fully protect against the unlikely possibility of having obtained a correlated design. 

Figure 15.7 Factor combinations for a completely randomized design investigating the effect of temperature. Fruit number is an arbitrarily assigned, qualitative factor. Numbers beside factor combinations indicate the time order in which experiments were run.

Figure 15.8 Sums of squares and degrees of freedom tree for the completely randomized design.

In the completely randomized design, a different fruit was randomly assigned a temperature, either 23°C or 27°C. Let us consider now a different experimental design. We will still employ the same number of experiments (20), but we will use only half as many fruit types, assigning each fruit type to both temperatures. Thus, each fruit will be involved in a pair of experiments, one experiment at 23°C and the... 

Up to this point, the randomized paired comparison design has not offered any great improvement over the completely randomized design. However, the fact that each fruit has been investigated at a pair of temperatures allows us to carry out a... 

Suppose someone comes to you with the hypothesis that shoes worn on the right foot receive more wear than shoes worn on the left foot. Design a randomized paired comparison experiment to test this hypothesis. How might it differ from a completely randomized design ... 

Only the first of two replicates is reported for each design. The UCC criterion measures the discrepancy from the ideal of one compound per cell in all ID, 2D, and 3D subspaces small values of UCC are desirable. No descriptors are required for a random design, hence the NA for not applicable in the table. 

The UCC and clustering methods require a descriptor set—BCUT or constitutional descriptors. As our implementation of UCC requires continuous descriptors, the 46 constitutional descriptors, which include discrete counts, were also reduced to either the first 6 or the first 20 principal components (PCs). Thus, the UCC algorithm was applied to the BCUT descriptors and either 6 or 20 PCs from the constitutional descriptors. In addition to these three sets, clustering was also applied to the 46 raw constitutional descriptors. The random design requires no descriptors. 

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