Statistical Methods in Medical Research 4ed

example discussed above we take a sample of 20 factories and second-stage
samples of 50 men in each of the 20 factories. If there is systematic variation
between the factories, due perhaps to variation in health conditions in different
parts of the country or to differing occupational hazards, this variation will be
represented by a sample of only 20 first-stage units. A random sample of 1000
men, on the other hand, would represent 1000 random choices of first-stage units
(some of which may, of course, be chosen more than once) and would consequently
provide a better estimate of the national mean.
A useful device in two-stage sampling is called self-weighting. Each first-stage
unit is given a probability of selection which is proportional to the number of
second-stage units it contains. Second-stage samples are then chosen to have
equal size. It follows that each second-stage unit in the whole population has an
equal chance of being selected and the formulae needed for estimation are
somewhat simplified.
Cluster sampling
Sometimes, in the final stage of multistage sampling, complete enumeration of
the available units is undertaken. In the industrial example, once a survey team
has installed itself in a factory, it may cost little extra to examine all the men in
the factory; it may indeed be useful to avoid the embarrassment that might be
caused by inviting some men but not others to participate. When there is no
sampling at the final stage, the method is referred to as cluster sampling. The
investigator has no control over the number of sampling units in the clusters and
this means that the loss of precision, compared with simple random sampling, is
even greater than that in multistage sampling.
Design effect
19.2 The planning of surveys 655
The ratio of the variance of an estimator from a sampling scheme to the variance
of the estimator from simple random sampling with the same total number of
sampling units is known as the design effect, often abbreviated to Deff. I n
Example 19.1 the Deff for allocation C is 0 000739=0 000803 ˆ 0 92. Another
way of looking at the Deff is in terms of sample size. The same precision could
have been achieved with a stratified sample of 92 people with allocation C as for
a simple random sample of 100 people. The stratified sample is more efficient
(Deff < 1) than simple random sampling and this will occur generally provided
that there is a component of variation between strata. The efficiency of stratified
sampling increases with the increasing heterogeneity between strata and the
consequent greater homogeneity within strata.
In contrast, multistage and cluster sampling will usually have a Deff > 1.
That is, a larger sample size will be required than with simple random sampling.