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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