Behavioural Surveillance Surveys - The Wisdom of Whores

Figure 6 : Procedures for calculating sampling probabilities for sample elements
(P i
) chosen using the various prototype sub-population survey sample designs
1. Selection of clusters PPS, with an equal
number taken from each cluster at the
second stage.
P i
= (m * M i
/M) * (n i
/N i
)
Where:
P i
= probability that a target group member
in cluster i was chosen for the survey;
m = number of sample clusters chosen;
M i
= expected measure of size for cluster i;
M = total measure of size for the survey
universe (M = ΣMi);
n i
= number of sub-population members
chosen in cluster i; and
N i
= total number of sub-population
members in the cluster i.
Note: Since it is expected that M i
and N i
will be equal,
they will cancel one another out. Since n i
is the same for
each cluster, all clusters will have an equal sampling
probability of n i
/M. Therefore this design results in a
self-weighed sample, and it will thus not be necessary to
apply sampling weights during analysis.
2. Selection of clusters with equal
probability, “take-all” strategy used at
second stage
P i
= (m/M)
Where:
P i
= probability that a sub-population member
in cluster i was chosen for the survey;
m = number of sample clusters chosen;
M = total number of sample clusters in the
sampling frame;
Note: Since all sub-population members present on
the randomly chosen day are chosen for the sample,
the second-stage sampling probability is equal to 1.0 and
is thus not shown above. Note also that this design
results in a self-weighting sample, and it will thus not be
necessary to apply sampling weights during analysis.
3. Selection of clusters PPS, sub-sampling
used at second stage
P i
= (m * M i
/M) * n i
/N i
Where:
P i
= probability that a sub-population member
in cluster i was chosen for the survey;
m = number of sample clusters chosen;
M i
= expected measure of size for cluster i;
M = total measure of size for the survey
universe (M = ΣMi);
n i
= number of sub-population members
chosen in cluster i; and
N i
= total number of sub-population members
in the cluster i.
Note: This design results in a non-self-weighting
sample, and it will thus be necessary to apply sampling
weights during analysis.
4. Selection of clusters with equal prob
ability, sub-sampling used at second stage
P i
= (m/M) * n i
/N i
Where:
P i
= probability that a sub-population member
in cluster i was chosen for the survey;
m = number of sample clusters chosen;
M = total number of clusters in the
sampling frame;
n i
= number of sub-population members
chosen in cluster i; and
N i
= total number of sub-population
members in the cluster i.
Note: This design results in a non-self-weighting
sample, and it will thus be necessary to apply
sampling weights during analysis.
B EHAV I OR A L S U R V EI L L A NC E SURV EY S CHAPTER 5
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