Information Technology Reference
In-Depth Information
Debates about the accuracy of the 2000 United States Census arose
from doubts about the fulfillment of these criteria.
1
“You didn't count
the homeless,” was one challenge. “You didn't verify the answers,” was
another. Whether we collect data for a sample or an entire population,
both these challenges or their equivalents can and should be made.
Kepler's “laws” of planetary movement are not testable by statistical
means when applied to the original planets (Jupiter, Mars, Mercury, and
Venus) for which they were formulated. But when we make statements
such as “Planets that revolve around Alpha Centauri will also follow
Kepler's Laws,” then we begin to view our original population, the planets
of our sun, as a sample of all possible planets in all possible solar systems.
A major problem with many studies is that the population of interest
is not adequately defined before the sample is drawn. Don't make this
mistake. A second major source of error is that the sample proves to have
been drawn from a different population than was originally envisioned.
We consider this problem in the next section and again in Chapters 2, 5,
and 6.
Sample
A sample is any (proper) subset of a population.
Small samples may give a distorted view of the population. For example,
if a minority group comprises 10% or less of a population, a jury of 12
persons selected at random from that population fails to contain any mem-
bers of that minority at least 28% of the time.
As a sample grows larger, or as we combine more clusters within a
single sample, the sample will grow to more closely resemble the popula-
tion from which it is drawn.
How large a sample must be to obtain a sufficient degree of closeness
will depend upon the manner in which the sample is chosen from the
population. Are the elements of the sample drawn at random, so that each
unit in the population has an equal probability of being selected? Are the
elements of the sample drawn independently of one another?
If either of these criteria is not satisfied, then even a very large sample
may bear little or no relation to the population from which it was drawn.
An obvious example is the use of recruits from a Marine boot camp as
representatives of the population as a whole or even as representatives of
all Marines. In fact, any group or cluster of individuals who live, work,
study, or pray together may fail to be representative for any or all of the
following reasons (Cummings and Koepsell, 2002):
1
City of New York v. Department of Commerce, 822 F. Supp. 906 (E.D.N.Y, 1993). The
arguments of four statistical experts who testified in the case may be found in Volume 34 of
Jurimetrics
, 1993, 64-115.
