Page 99 - DLIS401_METHODOLOGY_OF_RESEARCH_AND_STATISTICAL_TECHNIQUES

Methodology of Research and Statistical Techniques

Notes These imprecise populations are not amenable to sampling in any of the ways below and to
which we could apply statistical theory.
As a remedy, we seek a sampling frame which has the property that we can identify every
single element and include any in our sample. The most straightforward type of frame is a list
of elements of the population (preferably the entire population) with appropriate contact
information. For example, in an opinion poll, possible sampling frames include:
• Electoral register

• Telephone directory
Not all frames explicitly list elements of the population. For example, a street map can be used
as a frame for a door-to-door survey; although it doesn’t show individual houses, we can
select streets from the map and then visit all houses on those streets. (One advantage of such
a frame is that it would include people who have recently moved and are not yet on the list
frames discussed above.)
The sampling frame must be representative of the population and this is a question outside
the scope of statistical theory demanding the judgment of experts in the particular subject
matter being studied. All the above frames omit some people who will vote at the next election
and contain some people who will not; some frames will contain multiple records for the same
person. People not in the frame have no prospect of being sampled. Statistical theory tells us
about the uncertainties in extrapolating from a sample to the frame. In extrapolating from
frame to population, its role is motivational and suggestive.
“To the scientist, however, representative sampling is the only justified procedure for choosing
individual objects for use as the basis of generalization, and is therefore usually the only
acceptable basis for ascertaining truth.” (Andrew A. Marino). It is important to understand
this difference to steer clear of confusing prescriptions found in many web pages.
In defining the frame, practical, economic, ethical, and technical issues need to be addressed.
The need to obtain timely results may prevent extending the frame far into the future.
The difficulties can be extreme when the population and frame are disjoint. This is a particular
problem in forecasting where inferences about the future are made from historical data. In
fact, in 1703, when Jacob Bernoulli proposed to Gottfried Leibniz the possibility of using
historical mortality data to predict the probability of early death of a living man, Gottfried
Leibniz recognized the problem in replying:
“Nature has established patterns originating in the return of events but only for the most part.
New illnesses flood the human race, so that no matter how many experiments you have done
on corpses, you have not thereby imposed a limit on the nature of events so that in the future
they could not vary.”
A frame may also provide additional ‘auxiliary information’ about its elements; when this
information is related to variables or groups of interest, it may be used to improve survey
design. For instance, an electoral register might include name and sex; this information can be
used to ensure that a sample taken from that frame covers all demographic categories of
interest.

Did u know? The auxiliary information is less explicit; for instance, a telephone number
may provide some information about location.

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