QUALITATIVE AND QUANTITATIVE SAMPLINGRandom samplesyield samples most likely
to truly represent the entire population. They also
allow us to calculate statistically the relationship
between the sample and the population—that is,
the size of the sampling error. The sampling error
is the deviation between what is in the sample data
and an ideal population parameter due to random
processes.
Probability samples rely on random selec-
tion processes. Random selection for sampling
requires more precision, time, and effort than
samples with nonrandom selection. The formal
mathematical procedure specifies exactly which
person to pick for the sample, and it may be very
difficult to locate that specific person! In sampling,
random is not anyone, nor does it mean thought-
less or haphazard. For example, if we are using true
random sampling in a telephone survey, we might
have to call back six or seven times at different
times of the days and on different days, trying to
get a specific person whom the mathematically ran-
dom process identified.^4
This chapter does not cover all technical and
statistical details of random sampling. Instead,
we discuss the fundamentals of how probability
sampling works, the difference between good and
bad samples, how to draw a sample, and basic prin-
ciples of sampling in social research. If you plan to
pursue a career in quantitative research, you will
need more mathematical and statistical background
on probability and sampling than space permits here.
Five Ways to Sample Randomly
Simple Random.All probability samples are mod-
eled on the simple random samplethat first spec-
ifies the population and target population and
identifies its specific sampling elements (e.g., all
households in Prescott, Arizona, in March 2011).
Next we create an accurate sampling frame and we
then use a true random process (discussed later) to
pick elements from the sampling frame. Beyond cre-
ating an accurate sampling frame, the next difficulty
is that we must locate the specific sampled element
selected by a random process. If the sampled element
is a household, we may have to revisit or call back
five times to contact that specific selected household.
To select elements from a sampling frame, we
will need to create a list of random numbers that will
tell us which elements on it to select. We will need
as many random numbers as there are elements to
be sampled. The random numbers should range
from 1 (the first element on the sampling frame) to
the highest number in our sampling frame. If the
sampling frame lists 15,000 households, and we
want to sample 150 from it, we need a list of 150
random numbers (i.e., numbers generated by a true
random process, from 1 to 15,000).
There are two main ways to obtain a list of ran-
dom numbers. The “old-fashioned” way is to use
arandom-number table. Such tables are available
in most statistics and research methods books
including this one (see Appendix). The numbers are
generated by a pure random process so that any
number has an equal probability of appearing in any
position. Today most people use computer pro-
grams to produce lists of random numbers. Such
programs are readily available and often free.
You may ask, once we select an element from
the sampling frame, do we then return it to the
sampling frame, or do we keep it separate? Un-
restricted random sampling is called “random
sampling with replacement”—that is, replacing an
element after sampling it so it has a chance to be
selected again. In simple random sampling with-
out replacement, we “toss out” or ignore elementsSampling error How much a sample deviates from
being representative of the population.Random sample A sample using a mathermatically
random method, such as a random-number table or
computer program, so that each sampling element of
a population has an equal probablity of being selected
into the sample.Random-number table A list of numbers that has
no pattern and that researchers use to create a random
process for selecting cases and other randomization
purposes.Simple random sample A random sample in which
a researcher creates a sampling frame and uses a pure
random process to select cases so that each sampling
element in the population will have an equal probabil-
ity of being selected.