20 POPULATIONS AND SAMPLES
the sample, the number and location of observational units, the time schedule, and
so on. Sampling schemes that are good theoretically but undesirable from a practical
standpoint often are carried out so poorly that their superior theoretical advantages
are outweighed by mistakes and omissions made in executing the plan.
The second criterion for a good sampling plan is that it be done in an economical
fashion. For example, if a statistician wishes to estimate the average out-of-pocket
expense of households for medical care, a plan should be devised that results in an
accurate estimate of the average expenditure for the least cost. Cost in terms of
money or personnel time is an important consideration in sampling and is often a
major reason for the choice of a particular sampling plan.
A third criterion is that the plan should be such that it is possible to make inferences
from the sample to the population from which it was taken. For example, if we take
a sample and find that 75% of the patients in the sample are taking their medication
properly, can we infer that -75% of the patients in the population we sample from are
also taking their medication properly? This has been called measurability (see Kish
[ 19651). This criterion is often in conflict with the first two. As has been discussed
in this chapter, a simple random sample meets this criterion. Random samples, in
general, allow us to meet this criterion, but they may result in more complicated
formulas. But often, as we shall see in subsequent sections, it is not feasible or
economical to take simple random samples or even random samples.
2.4.2 Samples for SurveysThe size and location of a population often dictates what sampling method will be used
in surveys. For example, the population could be all English- or Spanish-speaking
noninstitutionalized adults in Los Angeles County in the fall of 2009. Here, the
population is very large and spread out. In contrast, a sample could be taken of all
medical school faculty at a given medical school in the fall of 2009. This population
will be much smaller in size and easily located.
In the first situation, where no listing of all adult residents in Los Angeles County
exists and the adults are widely spread out, the most cost-effective procedure is to
subcontract to a professional survey group. Devising a good sampling plan is too
expensive and time consuming. Simple random samples are not used in sampling
households from a large county such as Los Angeles because of both feasibility and
cost considerations. Samplers employed by professional surveyers are able to use
information from past surveys and are familiar with specialized sampling techniques
for large populations that save considerable time and effort. The resulting sampling
plan can still be random, but it is not a simple random sampling plan.
When a population is small and a list is already available, it is relatively easy to
obtain a survey sample. For example, if the observational units are medical school
physicians with full-time appointments, a list can undoubtedly be obtained. It is
advisable to check on whether the records are up to date and accurate before beginning.
A simple random sample can be taken, with random numbers obtained either from
a table such as Table A. 1 or from a statistical program. Systematic samples are also
commonly used for surveys from small populations.