Sampling
by David A. Freedman
Department of Statistics
University of California
Berkeley, CA 94720

     The basic idea in sampling is extrapolation from the part to the
whole--from "the sample" to "the population." (The population is some-
times rather mysteriously called "the universe.") There is an immediate
corollary: the sample must be chosen to fairly represent the population.
Methods for choosing samples are called "designs." Good designs in-
volve the use of probability methods, minimizing subjective judgment in
the choice of units to survey. Samples drawn using probability methods
are called "probability samples."
     Bias is a serious problem in applied work; probability samples min-
imize bias. As it turns out, however, methods used to extrapolate from a
probability sample to the population should take into account the method
used to draw the sample; otherwise, bias may come in through the back
door. The ideas will be illustrated for sampling people or business records,
but apply more broadly. There are sample surveys of buildings, farms, law
cases, schools, trees, trade union locals, and many other populations.

SAMPLE DESIGN
     Probability samples should be distinguished from "samples of con-
venience" (also called "grab samples"). A typical sample of convenience
comprises the investigator's students in an introductory course. A "mall
sample" consists of the people willing to be interviewed on certain days
at certain shopping centers. This too is a convenience sample. The reason
for the nomenclature is apparent, and so is the downside: the sample may
not represent any definable population larger than itself.
     To draw a probability sample, we begin by identifying the population
of interest. The next step is to create the "sampling frame," a list of
units to be sampled. One easy design is "simple random sampling." For
instance, to draw a simple random sample of 100 units, choose one unit
at random from the frame; put this unit into the sample; choose another
unit at random from the remaining ones in the frame; and so forth. Keep
going until 100 units have been chosen. At each step along the way, all
units in the pool have the same chance of being chosen.