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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