# Our estimate of this variation is as accurate as

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• apiccirello
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our estimate of this variation is as accurate as possible and is not inflated by being combined with other extraneous sources of variation. In the end, we want to do a calculation like a t-test, and the standard error in the denominator of this t-test will be our estimate of the natural chance-like variation in average weight gain for rabbits. The smaller we make our estimate of this chance-like variation, the more likely we are to detect a difference in the two varieties of rabbit food if a difference really exists. This is called increasing the power our test. We can gain power through controlling the experiment. The Price of Control: Scope of Inference The scope of inference refers to the population to which inference can reasonably be drawn based on the study. This population is the population from which the random sample used in the study was drawn. If only one breed of rabbit and one gender (male) is used, we might consider the results a random sample of results possible with this breed of male rabbit. We can comment only on this breed of male rabbit. If someone suggests that other breeds or females would behave differently with the diets, we have no counter-argument. We only have information about the breed of male rabbits we considered. If we had taken a random sample of rabbits from several breeds, we introduce the variation inherent in those breeds. Some breeds are smaller and more active than others, while others are larger and more sedate. This variation makes it more difficult for us to find a difference in weight gain due to diet if one exists. However, if we do find a significant difference in weight gain, we can say something about rabbits of different breeds, not just one special breed. Similarly, if we used males and females, our population of inference would be rabbits of either gender. Through control, the experimenter attempts to accentuate or make as visible as possible the planned, systematic variation between treatment groups, while at the same time reducing or removing as much chance-like variability as possible. The smaller the population of inference, often, the greater the control we have. Randomization: A second approach to handling the chance-like variability is through randomization. Clearly, it is not possible to remove all chance-like variation through our methods of control. Rabbits are still different, even if they are the same breed and gender; some will grow faster than others, regardless of the diet. Measurement error is always present even if the same scales and technicians are used. By randomly assigning the rabbits to the treatment groups, we will spread the chance-like variation among the treatment groups. This adds to the variation in each group, but it removes the bias that would otherwise doom the experiment. This random assignment of experimental unit to treatment group is essential for an experiment and distinguishes it from an observational study. In an observational study, the experimental units or subjects are not randomly assigned to the treatment groups.

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