Post-enumeration Survey (PES) - Statistics South Africa

Statistics South Africa
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11. The relation between the undercount rate and the adjustment factor is the following:
1
ADJ _ FACT = 1 − undercount rate
In other words, the adjustment factor is the reciprocal of the complement of the undercount rate.
For example, an undercount rate of 2% implies an adjustment factor of 1,0204. Likewise, an
undercount rate of 8% implies an adjustment factor of 1,0870, and an undercount rate of 14% implies
an adjustment factor of 1,1628, and so forth.
12. Another way of viewing the adjustment factor is the following:
Adjustment Factor =
PES _ POP × CENS _ POP _ CORR
MATCHED _ POP
CENS _ POP _ UNCORR
If we consider the quantity
MATCHED _ POP
PES _ POP
as the 'Coverage Rate', then:
⎡ 1 ⎤ ⎡
⎤
Adjustment Factor = ⎥ × CENS _ POP _ CORR
⎢
⎢
⎥
⎣Cov
Rate⎦
⎣CENS
_ POP _ UNCORR ⎦
While the quantity inside the first bracket is clearly a correction for under-enumeration, the quantity in
the second bracket – which is the proportion of the census population that was correctly enumerated,
i.e., not erroneously included – serves as a correction for over-enumeration.
Hence, the final adjusted population is in effect calculated as follows:
Adjusted Population = under-enumeration correction factor × overenumeration
correction factor × census count
Also note that the under-enumeration correction factor is always ≥ 1 and the over-enumeration
correction factor is always ≤ 1. The overall factor can theoretically fall on either side of 1, depending
on which is higher, the undercount or the overcount.
13. The probabilities of inclusion and omission of a person are calculated as follows:
Post Enumeration Survey (PES)