Suppose that in an experiment there are a total of N plots. Consider the total df (N-l). We use these in three
ways:

 (i) Estimating the error or random variance, s2
 (ii) Controlling, or identifying and allowing for causes of variation. This includes blocking,
 covariance adjustment, possible losses of plots.
 (iii) Answering questions through treatment comparisons. Here, questions include those relating to
 main effects and interactions, but also possibly the modification of treatment effects by
 environments.

 If we consider (i) first then it is usually accepted that a good experiment should have at least 12 df for error
 (some might say 10 or 15 instead of 12). It is equally important to recognize that there is very little benefit
 in having more than 20 df for error. An experiment with more than 20 df for error is inefficient. Surplus d.f
 should be transferred to (ii) to reduce s2 and hence improve precision or to (iii) to provide answers to more
 questions.

 For example, a simple Randomised Complete Block Design with 4 blocks and 12 treatments in each block
 is an inefficient design because it allocates 33 df to error. To redesign the experiment to make better use of
 the resources, we could try to use more df in (ii) or (iii).

 One way of using more df in (ii) would be to use smaller blocks, dividing each complete block of 12
 treatment plots into incomplete blocks of 4 or 6 treatment plots. The construction of incomplete block
 designs [(see Mead (1988) chapters 7 and 15] but will be worthwhile only if reducing block size reduces s2
 as should often be possible. More df could also be used in (ii) by identifying covariates which might
 explain some of the plot-to-plot variation.

 More df could alternatively be used in (iii) by including an additional treatment factor at two levels and
 assessing the main effect of the factor and interactions with the original treatment factors. The upper level
 could be applied to six treatments in block 1 and the lower to the other six treatments with the pattern
 reversed in block 2, and the whole pattern or a similar one repeated in blocks 3 and 4. Further discussion of
 such confounded designs is given in Mead (1984, 1988).

 I believe it is crucial in OFR that we do not simply transfer the often thoughtless and inefficient recipe
 designs used widely in research station experimentation. We must design experiments efficiently to use
 resources fully.

 On station experiments are often regarded as good. I believe, on the contrary that they are often
 unimaginative, inefficient and boring and they achieve information only because of the overall high level
 of control and by being big.

 Good designs could, in fact, reap very much greater rewards in OFR than they have been allowed to on
 research stations.

 3. Plot Sizes

 3.1 Plot size, choices and implications

 It is quite widely believed that the variability which results when using small plots for OFR experiments is
 such as to make small plot OFR experimentation inappropriate. It is not clear that there is anything peculiar
 about the variability of plots on farms except that it is rather larger than that on research stations. The
normal statistical expectation would be that the relation between the plot standard deviation, s, and plot
area would be of the form

 s = K/ 4Area.