PHL 120 – Martin, Chapter 3 SAMPLING
1. A great many of the questions which interest people in both the natural and
social sciences - in medical trials, animal studies, marketing and politics –
concern the proportion, expressed as a percentage, of individuals in a
population which have some particular property.
2. Notes on terminology:
i. We are seldom interested in proportions near the 100% level, because in
these cases we usually already know that almost every individual has the
property in which we’re interested. Sometimes, especially in medical
epidemiology, we are interested in proportions near the 0% level. (E.g. of
Jenner’s study of smallpox.)
ii. A population is any class of objects or events; not necessarily people.
Similarly, by individuals we simply mean any particular member of the
class; these will not be people unless the population in questions is a
population of people.
iii. Properties are characteristics which we believe some individuals in a
population have.
3. Martin provides some examples of questions about proportions on p. 53. Here
are some others:
How many smokers are likely to develop lung cancer?
How many non-smokers are likely to develop lung cancer?
How many wolf cubs survive to reach maturity?
How many people in Birmingham will want to buy the latest Frank Stitt
cookbook during the next six months?
What proportion of the stimulus package home-owners’ rebate will
Americans save rather than spend in 2009?
4. We cannot answer these questions by examining every smoker, or every non-
smoker, or every wolf cub, or everyone in Birmingham or America. To answer
these questions, we must perform induction based on sampling a sub-set of the
population. If we sample properly, our aim is to establish a good inductive
argument of the following form:
Among 600 wolf cubs tagged at birth, 200 were still found alive at
maturity.
Therefore, about 33% of wolf cubs survive to maturity.
5. There are many conditions necessary for proper sampling. Obviously, if one
sampled only wolf cubs born in a drought stricken area, one would arrive at an
unreasonably low estimate of young wolf cub mortality in general. Conversely, if
one sampled only wolf cubs born in zoos, one would obtain an unreasonably
high estimate. In either of these cases, the inductive argument above would fail
to justify its conclusion.
