Design Issues When conducting a statistical survey, one is hoping to make inferences of
some sort. That nature of the inferences one would like to make helps to guide
the process of designing a study. There are several aspects of inferential
objectives that commonly occur: a specific population is defined; degrees of
similarity or distinctness between sub-populations are inferred; certain
traits of individuals or environments can be used to predict other traits of
interest.
In addition, there are several scientific objectives of such studies. An
intelligently designed study can be used to make inferences about correlations
or even about causal relationships between variables. Even a small study that
does not provide the sort of data necessary to make desirable inferences can
be used in several ways to assist in the design of larger studies:
relationships suggested by a small study can be investigated in a larger study
by making the proper observations and measurements; estimates of variance and
other relevant parameters obtained in a smaller study can be used to help
determine the size of a larger study needed to achieve the desired level of
confidence about one's inferences.
Beyond determining what inferential objectives are of interest, one must
have some understanding of the nature of the stochastic processes underlying
one's observations. In the case of parametric models, one must have some sort
of evidence that the distributions in one's model are reasonable
approximations of what one is observing. This can include issues of
independence and of stationarity of random variables. (Stationary random
variables have distributions that do not depend on location in time or
space.)
In order to understand a stochastic process, one must have some insight
into the process by which one is observing the underlying process of interest.
In the case of a population survey, one wants to know what sort of biases may
be caused by the process of observing. For example, say that a coin (that is
not necessarily fair) has been tossed 1000 times, and that you have observed
100 of the outcomes. If the selection process by which observations are
recorded is independent of the actual state of the observations then the
likelihood of heads or tails can be estimated without bias from the sample of
100. But, if heads outcomes are twice as likely to end up in the observed
sample as are tails outcomes, then estimates, of the likelihood of heads
or tails, made under the assumption of independence will be very biased.
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| Contributed by: David Caccia
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