Arrangements versus designIn the design and analysis of experiments, design and arrangement are often confused. This is true because statistical textbooks often do not make the distinction. Furthermore, the procedures used to analyse experiments take both design and arrangement into account. The design of the experiment dictates how treatments are randomized among experimental subjects or units. The arrangement of the treatments is the relationship of the treatments to each other. In the most typical arrangement, the treatments will be qualitatively different from each other. For example, treatments in a pesticide trial will be composed of different compounds plus a control. These different treatments could be applied randomly using one of several designs. On the other hand, treatments could be quantitatively different. For example, treatments in another pesticide trial will be composed of the same compound applied at different rates. The analysis of treatments that are quantitatively different will be performed using a different procedure than those that are qualitatively different. Compare Complete Randomized Design (CRD) with Regression--treatments from a continuous range. The analyses are different because the statistical null hypotheses are different. In the qualitative case, the null hypothesis is that the the treatment means are not different. In the quantitative case, the null hypothesis is that an increasing (or decreasing) amount of the treatment has no effect. One hypothesizes about the effect of several discrete effects, the other about a continuous effect of the treatment. Yet another common arrangement of treatments is the factorial where treatments are actually combinations of treatments. For example a thinning experiment could test the use of a bloom treatment, a post-bloom treatment, both, or neither. The combinations are then randomly assigned to experimental units rather than the simpler effects assigned. Many statistics books will devote a chapter or more to the factorial arrangement, and some books may actually lead to confusion with the Randomized Complete Block (RCB) design. You can have, and often do have, a factorial arrangement of treatments laid out on a RCB design. I provide two examples of factorial arrangements: on a CRD and on a RCB.
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