The Advantages of Planning Experiments

It will have been apparent that none of these statistical designs for experiments can be applied without the appropriate forethought and plarming. They cannot be superimposed on a hotch-potch of random results. 

To take an example of this, consider the case discussed in Chapter XIII (a) where we tested 7 treatments in blocks of 3. The variance of the comparison of any two corrected means was (6/7) ok, = 0.857ok, where ok was the error variance of a single observation within blocks. 

Now suppose that instead of starting off the experiment with the full number of treatments (7) we had begun with only 4 and had afterwards decided to test the remaining 3. Our first 4 could be tested with the design given in Table 13.3, when the variance of the comparison of any two of these means would be 

When we consider that the experiment in two stages has taken 24 runs as compared with 21 for the experiment in one stage, it is evident that the latter has been much more satisfactory. 

In parenthesis, a comparison might be ihade with the classical type of experiment using a single standard throughout. The nearest approach to a balanced design calls for 6 blocks, all contaimng the standard and two of the remaining 6 treatments. Each of the latter therefore occurs twice. The total number of runs 

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