Sampling Strategies

     We now discuss the details of various sampling schemes. 
These include simple random sampling, stratified random sampling
and cluster sampling. 

Simple Random Sample

     When every member of a population has the same chance of
being included in a sample, we are using simple random sampling. 
This is the easiest kind of sampling scheme to understand, but it
is often difficult to execute and costly to implement.  
     In order to select a random sample, we must have a list of
all members from a population.  We select the sample using a
random numbers table.  It is often difficult to assemble these
lists.  Since every observation has the same opportunity to be
included, the elements of the sample will come from all places in
which the population resides.  This can make contacting the
members of the sample expensive.
     There are ways to approximate drawing a simple random sample
without actually compiling the lists and using a random numbers
table.  One approach is to use lists that are already compiled. 
Telephone surveys are an example.  The telephone company has
already compiled the list.  It is the list of telephone numbers.
     One way that using these preexisting lists may introduce
bias into the sample is that all members of the population may
not be included in the list.  Anyone who does not have a
telephone will be excluded.  These are usually the poor.  Some
lists may also exclude those with unlisted numbers.
     Another way that bias may enter a simple random sample
occurs no matter how the list was formed.  Some people are easier
to contact and more willing to participate than others.  People
who work are unlikely to be included in a daytime survey.  There
are usually differences between those who agree to respond and
those who refuse?


Stratified Random Sampling

     In stratified sampling the population is divided into
subunits before the random sample is drawn.  This was done to
draw sample two above.  The population was stratified into rural
and urban subpopulations before the sample was drawn.  The
subpopulations are called strata.  
     There are several reasons why we may want to draw a
stratified sample:

1.  We want to assure that the estimated parameters have a
certain precision for the subpopulations.  It may be necessary to
sample a large proportion of people from small strata and a
smaller proportion from large strata.  A case control study is an
example of a stratified sample.


2.  Sampling problems may differ for various subpopulations.  For
example, special approaches may be required for those in prison,
in mental institutions or the homeless.

3.  We may gain precision for a given sample size.  This will be
the case if the observations within a stratum are homogeneous
with respect to the variables of interest.  

     We can sample proportionate to stratum size, but this is not
necessary.  If we want to assure that the parameter estimates
from the strata are of equal precision, we will not sample
proportionately.  
     If our goal is to estimate a population parameter, we must
know the ratio of the sample size to the population size for each
stratum.  If we are exploring associations between variables, we
must control for stratum in the analysis. 


Cluster Sampling

     In cluster sampling the population is first divided into
subunits.  Subunits are then selected to be in the sample.  All
elements within the selected subunits may be included in the
sample, but it is also possible to sample from within the
subunits.  
     The primary reason for drawing a cluster sample is to
conserve resources.  It is more efficient to sample heavily in a
few regions than to sparsely throughout the population.
     Political or geographical units often serve as the clusters.

These units might be villages within a state or county or
neighborhoods or city blocks within a city.
     Although cluster sampling may be more efficient than simple
random sampling in terms of finding the elements, it usually
requires a larger total sample than does simple random sampling
to achieve the same precision.  The following rules apply:

1.  The required sample size increases as the differences among
the clusters increases.

2.  The required sample size increases as the clusters become
more heterogeneous.

     The required sample size will be smallest if each cluster
seems to be a random sample from the entire population and there
are no differences among the clusters.  Stratification prior to
sampling can assist in accomplishing these goals.


Level of Random Assignment

     We have emphasized the importance of assigning individuals
to treatments randomly.  In evaluation a violation of this often
occurs which is closely related to the sampling issues we have
discussed.  This is the level at which we do the randomization. 
We are often forced to assign villages, schools, classrooms or
clinics to the treatment groups rather than the individual
subjects.  Mass media campaigns are examples of when this is
necessary.  It is not possible to expose some people in an area
and not others.  Similarly, it is often not possible to give some
students in a classroom one treatment and others another.
     As in cluster sampling our goal in these situations is that
each cluster (classroom or village) resemble the total population
and that the clusters are all similar.