treatment groups.
As an example, if we looked at rabbits at Farm A who are presently being fed Diet A and rabbits at Farm
B who are presently being fed Diet B, we might find that the average weight gain for the rabbits at Farm A (on Diet A) had a
greater average weight gain.
However, the diet and farm are inextricably confounded.
We could never say that Diet A was
better than Diet B, since any weight gain could be a result of other aspects of rabbit life at the two farms.
If, in the end, we
want to say that one diet produces greater average weight gain in rabbits than the other, then randomization is essential.
Randomization plays other roles in our experiment.
We should place the rabbit cages in our designated locations
through a random process.
This keeps the lurking variables of heat, light, air flow, and other unknowable variables from
biasing the results.
These unknown variables can produce systematic, unplanned variation if randomization is not used.
The
effects of these variables, if any, is distributed to the two treatment groups by this randomization process.
This form of
randomization is our protection against bias (unplanned, systematic variation) in the experiment.
Finally, a randomization process creates the probability models we use for the basis of
hypothesis tests.
If the null
hypothesis is true (diet has no effect on average weight gain), then the variation we see between treatment groups must all be
of the chancelike variety.
We have estimated the size of this variation, and we build our hypothesis tests around it.
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Chapter 5:
Producing Data
Both of these types of randomization are essential to a good experimental design.
A third type of randomization,
random sample of experimental units from the population of inference, is not essential and is often not possible.
However, if
a random sample is taken, we can make inferences to the population once we have our result.
Replication:
Replication in an experiment just means using more than one experimental unit.
In this context, it does not mean
repeating the whole experiment multiple times.
Each additional rabbit is called a replicate.
We must have a way to estimate
the size of the chance variation and we need at least two values to compute a standard deviation.
Without replication, there is
no way for the experimenter to estimate the chancelike variation to compare to the systematic, planned variation between
treatment groups.
The more rabbits used for each diet, the more accurate is the estimate of the natural variation in weight
gain.
There is a second benefit of using more rabbits; the greater the number of replicates in each treatment group, the
smaller the standard error used in the ttest, since the estimated variance of the mean weight gain of n rabbits is the estimated
variance for single rabbits divided by n.
This corresponds to a reduction in the estimate for the size of the chancelike
variation in the mean increase in weight.
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 Fall '12
 SonjaCox
 Sampling Methods, AP Statistics, experimental units

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