Blocking:The final method for managing the variability inherent in an experiment is through blocking. Blocking is more complicated than control, randomization, and replication. Suppose, due to availability, we were forced to use two different breeds of rabbits instead of just one. We have four Californian and four Florida White rabbits for use in this experiment. We believe that the Californian will grow faster than the Florida White and so the weight gains for these four rabbits will be larger than that of the other four, regardless of the diet. For example, we might expect the average weight gain for Florida White rabbits to be about 10 ounces less than the average gain for the larger Californian rabbits. However, we don't think there will be an interaction between breed and diet. This means that the effect of each diet on the rabbits' growth will be the same additive amount. We might suspect that, for example, Diet A will add 6 ounces to the weight gain for both California and Florida White rabbits. The variability due to the two breeds is not chance-like; it is systematic, unplanned variation. We can turn this variation into chance-like variation by our random assignment process, but the variation caused by having two different breeds will be included in our estimate of chance variation, inflating it and reducing the power of our test. A better solution comes from the process called blocking. We will use the breed as a blocking variable. We are not really interested in the effect of breed, so we think of breed as a nuisance variable. We want to estimate the amount of variation added by having two different breeds, and remove it from our estimate of the chance-like variation (reducing our standard error) by the process of ANOVA. In AP Statistics students are taught that a good experiment requires Control, Replication, and Randomization. Each of these attributes offers the experimenter a way to manage the inescapable variability inherent in the experimental process. The planned, systematic variability is emphasized by controlling extraneous sources of variation, while the chance-like variability is managed by randomization and reduced by replication and control. Finally, the unplanned, systematic variability that an destroy our results can be managed by blocking when its causes are recognized prior to the experiment and through randomization in any event. The experimenter must always pay careful attention to the design of the experiment, since the method of analysis is determined by the manner in which the experimental units are randomized to treatments. The way you randomize is the way you analyze.
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