Behavioural Surveillance Surveys - The Wisdom of Whores

Design effects
The formula given for calculating sample
sizes includes a term D, for the design effect.
This is used in multi-stage sample designs, to
correct for the difference between the chosen
design and a simple random sampling design
(in which every member of the universe is
enumerated and the sample is chosen at
random from all members of the universe).
D may be simply interpreted as the factor by
which the sample size for a cluster sample
would have to be increased in order to produce
survey estimates with the same precision as
a simple random sample.
The magnitude of D depends upon two
factors:
the degree of similarity or homogeneity of
elements within primary sampling units
the number of sample elements to be taken
from each PSU
The initial factor, the homogeneity of
elements within PSUs, is a population characteristic
over which the survey manager has no
control. In general, individuals within one PSU
tend to be more similar to one another than
they may be to individuals in another PSU.
For example, 10 respondents taken from a
single brothel with a 100 percent condom use
rule will probably report more similar levels
of consistent condom use that 10 respondents
taken from 10 different brothels, some of
which enforce condom use and some of
which don’t. The prudent course is therefore
to assume that some degree of homogeneity
within PSUs exists. The second parameter,
the number of individuals chosen per PSU,
is largely within the control of the survey
manager, and is an important consideration
in the sample design for any survey. This is
discussed further in the section titled Number
of PSUs and sample sizes from each, later in
this chapter.
To calculate the design effect accurately for
the two-stage sampling designs commonly
used in BSS, it is necessary to be able to
estimate the variation of behavior between
individuals within a single PSU, as well as
the average variation in behavior between
all selected PSUs. This information is used
to calculate the intra-class correlation
coefficient (ρ), as follows.
ρ = (standard deviation (SD) for variation
between PSUs) 2
(SD for variation between PSUs) 2
+ (SD for variation within PSUs) 2
The design effect D is then calculated as:
D = 1 + (number sampled per PSU - 1) ρ
Information on the variations in behavior
within and between PSUs is rarely readily
available, at least during a first survey round,
so the use of a “default” value is recommended.
Assuming that cluster sample sizes can be kept
moderately small in a given survey (e.g., not
more than 20-25 individuals per PSU), the use
of a standard value of D = 2.0 should adequately
compensate for the loss of accuracy resulting
from two-stage sampling designs. In fact, the
real design effect may be smaller than this.
Since a smaller design effect will lead to
smaller sample sizes, it is worth calculating the
design effect accurately for subsequent survey
rounds, using data collected during the first
survey round and the formula given above.
B EHAV I OR A L S U R V EI L L A NC E SURV EY S CHAPTER 4
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