Interlude: Assessing the Effects of Blocking
In Chapter 3 we modeled blocks as a random factor, one in which the levels that actually appear in the experiment are considered a random sample from all levels. However, the concept of “random factor” can sometimes be puzzling, as most of the time we do not actually take a random sample of blocks. Rather, we choose blocks to represent a wide variety of situations. In a sense the concept of a random factor is a fallacy (see Section 3.8.4). That is, the important implication is that blocking induces a correlation in the design. This only makes sense, as experimental units within a particular block should behave similarly, and hence will be correlated. This correlation can be modeled directly, or can arise as a byproduct of assuming that blocks are a random effect. In either case we end up with the similar analyses.
Whether blocks are random or are fixed, the important point is that a correlation structure is induced. As far as the model calculations go – variances, covariances, etc, they are quite similar.
KeywordsRandom Factor Experimental Unit Randomization Test Technical Note Random Block
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