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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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.
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 chancelike; it is systematic, unplanned variation.
We
can turn this variation into chancelike variation by our random assignment process, but the variation caused by having two
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 Fall '12
 SonjaCox
 Sampling Methods, AP Statistics, experimental units

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