Replication

We have already used this word, even before defining it, as we shall do now. Replication is repetition with some difference. When we speak of repetition, we normally imply a sequence in temporal order; what we do now, we may do after a lapse of time, no matter how long. This is replication of the simplest kind. When repetition is concurrent or simultaneous, that is replica­tion too. For instance, in the agricultural experiments we have discussed, in which different varieties of rice were tested for yield, we find in the experimental setup that each variety of rice was cultivated not in only one, but in four different plots, under identical conditions, but physically separated. The yield from each plot can be compared with that from any one or all of the other plots. But, as far as the yield of that particular variety is concerned, the statistical average of yield from all four plots is rel­evant, and for this purpose, the experimental details are equiva­lent to four repetitions, though done simultaneously.

Another extension of replication is the case of paired compar­ison experiments we discussed in Chapter 7, for testing a plant food, where A and A¹ were two flowering plants of one kind, B and B¹ of the second, C and C¹ of the third, and so on. They were experimented on under identical conditions. All these tests of ten comparisons were virtually ten replications in the sense that they were all one experiment testing the benefit of one plant food on one class, namely flowering plants, though this class con­tained ten varieties. Here we had identical conditions relative to the treatment, but variety relative to the recipient of the treat­ment. The intention of the experiment was to form a generaliza­tion of the benefit of a particular plant food on flowering plants. It was one experiment with ten replications.

In the generalization of the one-cause-one-effect, x—y relation, the effect on the dependent variable, y, of changing the indepen­dent variable, x (usually a quantity), is the essence of the experi­mentation. The hardware part of the experimental setup, the calibration, the measuring devices, and so forth, remains unal­tered. But for the change in parameters, experiments conducted are virtually a series of replications. Replication with parametric varieties, or simply parametric replications, may be an apt name for these.

Now, what is the purpose of replication? Common to all three variations we discussed, we may say that replication increases the confidence of the experimenter in his inferences. Whether this can be quantified into a confidence factor, we will discuss in Chap­ter 19, though we may say at this point that the more the replica­tion, the more the confidence, with the highest confidence still falling short of certainty, just like the highest number is still not infinity. The relevant, practical question is not how many, but how few, replications are necessary. For the purpose of obtaining sufficient confidence to make a statement or attempt a generali­zation, what should be the minimum level of confidence? Statisti­cians have worked out the answer to this question in various situations relative to availability of data; we shall deal with these in Chapter 19.