Appendix D: Sampling error The undercount rates presented in this
report are subject to a number of sources of error. While any survey is subject to errors
at various phases, there were some additional problems relating specifically to the 1996
PES in South Africa, as have already been discussed. Some of the possible sources of error
in this PES include:
- Respondent errors in answering questions.
- Enumerator errors in identifying households that
should be included.
- Errors made in matching PES and census
questionnaires.
- Errors made in entering the data.
- Errors arising from the imputation of missing data.
- Other errors introduced through other assumptions
made in the calculations.
- Sampling error, that is, the error arising from
collecting data for the PES from a sample of the population rather than the whole
population.
Estimates of sampling error have
not been included in the body of this publication as sampling error constitutes only one
source of error and providing sampling errors may have given a misleading impression of
the accuracy of the data. However, the sampling errors are included here for information.
These estimates were calculated based on the methodology used in selecting the PES sample.
Table D.1: Sampling errors for
undercount by province
|
|
|
95% confidence limits |
Province |
Undercount
rate (%) |
Sampling
error |
Lower
limit |
Upper
limit |
Western Cape |
8,69 |
0,73 |
7,23 |
10,15 |
Eastern Cape |
10,57 |
0,64 |
9,29 |
11,85 |
Northern Cape |
15,59 |
2,52 |
10,55 |
20,63 |
Free State |
8,75 |
1,00 |
6,75 |
10,75 |
KwaZulu-Natal |
12,81 |
0,68 |
11,45 |
14,17 |
North West |
9,37 |
0,59 |
8,20 |
10,54 |
Gauteng |
9,99 |
0,49 |
9,01 |
10,97 |
Mpumalanga |
10,09 |
1,04 |
8,01 |
12,17 |
Northern Province |
11,28 |
0,83 |
9,62 |
12,94 |
South Africa |
10,69 |
0,27 |
10,15 |
11,23 |
The confidence intervals on the
undercount rate mean that there is a 95% chance that the population of South Africa
(estimated to be 40,58 million) is between 40,34 million and 40,83 million. However, as
mentioned above, this does not take into account the sources of error other than sampling
error.
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