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 ttest, and the standard error in the denominator of this ttest will be
our estimate of the natural chancelike variation in average weight gain for rabbits.
The smaller we make our estimate of this
chancelike 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 counterargument.
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 chancelike variability as possible.
The smaller the population of inference, often, the greater the control we have.
Randomization:
A second approach to handling the chancelike variability is through randomization.
Clearly, it is not possible to
remove all chancelike 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 chancelike 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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 Fall '12
 SonjaCox
 Sampling Methods, AP Statistics, experimental units

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