All of the aspects of the experimental setting mentioned so far can be considered natural
chancelike variation.
There is another source of essential variation:
the systematic difference in the rate of growth that is a result of the
different diets.
This is a variation we want to investigate.
One way to think about the goal of the experiment is that we want
to know if the variation that is a result of the diet is larger than the variation that is due to all the natural variation inherent in
rabbit growth.
In designing our experiment, we want to accentuate this planned, systematic variation, while reducing the
natural chancelike variation.
This chapter considers some of the methods the experimenter has for managing these three sources of variation in
the example experiment.
The methods are Control, Randomization, Replication, and Blocking.
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View Full DocumentChapter 5:
Producing Data
Control:
We control the experiment by organizing the structural components of the experiment to remove as many sources of
chancelike variation as possible.
We want to keep the experimental units (in this example, the rabbits in their cage) as
similar as possible.
We would like to use only one breed of rabbit.
We might also prefer to use just one gender of rabbit,
since male and female growth patterns may differ.
We certainly want to keep the cages in a single location so that the effects
of heat, light, air flow, and other unknowable affects will be as consistent as possible.
As much as possible, we want the only
difference among the rabbits to be the diet they are receiving.
To control the measurement error, we want to use the same scale when measuring the food each day.
Similarly, it is
important to use the same scales to measure the weights of the rabbits before and after the experimental regimen.
We would
prefer to use the same technician as well.
In the end, no matter how much control we have in our experiment, some chance
like variation remains.
It is the natural variation in average weight gain for our rabbits.
By control, we try to make sure that
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
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 Fall '12
 SonjaCox
 Sampling Methods, AP Statistics, experimental units

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