3240.1 - Housing Choices, NSW, Oct 2004  
ARCHIVED ISSUE Released at 11:30 AM (CANBERRA TIME) 01/04/2005   
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SAMPLING VARIABILITY


ESTIMATION PROCEDURE

1. Estimates derived from this survey were obtained using a post-stratification procedure. This procedure ensured that the survey estimates conformed to an independently estimated distribution of the population, by the number of adults and children within the household, and part of state, rather than the distribution among respondents.


RELIABILITY OF ESTIMATES

2. Estimates in this publication are subject to non-sampling and sampling errors.

Non-sampling errors

3. Non-sampling errors may arise as a result of errors in the reporting, recording or processing of the data and can occur even if there is a complete enumeration of the population. Non-sampling errors can be introduced through inadequacies in the questionnaire, non-response, inaccurate reporting by respondents, errors in the application of survey procedures, incorrect recording of answers and errors in data entry and processing.

4. It is difficult to measure the size of the non-sampling errors. The extent of these errors could vary considerably from survey to survey and from question to question. Every effort is made in the design of the survey and development of survey procedures to minimise the effect of these errors.

Sampling errors

5. Sampling errors are the errors which occur by chance because the data were obtained from a sample, rather than from the entire population.


ESTIMATES OF SAMPLING ERRORS

6. One measure of the variability of estimates which occurs as a result of surveying only a sample of the population is the standard error.

7. There are about 2 chances in 3 (67%) that a survey estimate will differ by less than one standard error from the number that would have been obtained if all dwellings had been included in the survey. There are about 19 chances in 20 (95%) that the difference will be less than two standard errors.

8. Linear interpolation can be used to calculate the standard error of estimates falling between the sizes of estimates listed in the table.

9. The standard error (SE) can also be expressed as a percentage of the estimate. This is known as the relative standard error (RSE). The relative standard error is determined by dividing the standard error of an estimate SE(x) by the estimate x and expressing it as a percentage. That is—(where x is the estimate)


Equation - RSE(x)=100*SE(x)/x





10. Proportions and percentages formed from the ratio of two estimates are also subject to sampling error. This size of the error depends on the accuracy of both the numerator and the denominator. The formula for the relative standard error (RSE) of a proportion or percentage is—


Equation - RSE (x / y) = square root of [RSE (x)] squared - [RSE (y)] squared





11. Only estimates with relative standard errors of 25% or less, and percentages based on such estimates, are considered sufficiently reliable for most purposes. However, estimates and percentages with a larger RSE have been included, preceded by * (RSE between 25% and 50%) or ** (RSE greater than 50%) to indicate that they are subject to high standard errors and should be used with caution.

STANDARD ERRORS OF ESTIMATES OF NSW HOUSEHOLDS, October 2004
Size of estimate
Standard error
Relative standard error
(households)
no.
%
1,000
643
64.3
1,500
802
53.5
2,000
936
46.8
2,500
1,054
42.1
3,000
1,160
38.7
3,500
1,257
35.9
4,000
1,347
33.7
5,000
1,511
30.2
8,000
1,918
24.0
10,000
2,144
21.4
20,000
3,007
15.0
30,000
3,647
12.2
50,000
4,626
9.3
100,000
6,325
6.3
200,000
8,554
4.3
300,000
10,154
3.4
500,000
12,534
2.5
1,000,000
16,522
1.7
2,000,000
21,538
1.1
3,000,000
25,023
0.8


12. Where differences between data items have been noted in the Summary of Findings, they are statistically significant unless otherwise specified. In this publication a statistically significant difference is one where there are 19 chances in 20 that the difference noted reflects a true difference between population groups of interest rather than being the result of sampling variability.