A small scale preliminary survey, done BEFORE carrying out a full, large scale random sample survey, is called a PILOT sample or a Pilot Study. This is extremely useful for many purposes. We highlight THREE such purposes here:
The table shows the standard error of estimate based on a pilot study with sample size of only 25. It shows that this can vary from 12% to 20% -- still this narrows the range of from 0 to 100% by quite a bit. The second column shows the sample size required to achieve accuracy of plus or minus 5% with 95% confidence. At p=10%, only 144 SS is required while at the worst case of 50%, a full 400 SS is required for this accuracy. A preliminary pilot study can help in selecting a more accurately targeted sample size and save money.
One special consideration arises for cases where p is very small, near 0 (or equivalently, very large, with p near 1). For small values, absolute error sometimes is not the relevant consideration -- to say that with 95% confidence, p is less than 5%, conveys no information when p is known to be small, around 1% in the population for example. Achieving higher accuracy in such cases requires huge sample sizes. To avoid this, it is useful to specialize to a subpopulation where the incidence is higher. For example, if one is study people with certain types of handicaps, one might look at a population of hospital patients, where one is more likely to find the desired typed of people being surveyed. By a targetted smaller subpopulation with higher incidence, one can get a higher sampleing rate for the desired characteristic, and thereby get a more accurate survey.
Action without change? On the use and usefulness of pilot experiments in environmental management — Raphaël Billé: One of the most common approaches to environmental action consists in designing and implementing pilot experiments, which aim at testing new practices and organisations.
Sample Size for Pilot Studies — Lengthy discussion of how to choose pilot study sample size.
The importance of Pilot Studies — Edwin R. van Teijlingen and Vanora Hundley
Wiki Pilot Experiment — Brief and not very informative