
TECHNICAL NOTE: SAMPLING VARIABILITY
ESTIMATION PROCEDURE
1. Estimates derived from this survey were obtained using a poststratification 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 nonsampling and sampling errors.
NONSAMPLING ERRORS
3. Nonsampling 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. Nonsampling errors can be introduced through inadequacies in the questionnaire, nonresponse, 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 nonsampling 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 error is the error which occurs by chance because the data were obtained from a sample, rather than from the entire population.
ESTIMATES OF SAMPLING ERROR
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 (see table below).
7. There are about two chances in three (67%) that a survey estimate is within one standard error of the figure that would have been obtained if all households/persons had been included in the survey. There are about nineteen chances in twenty (95%) that the estimate will lie within 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 can also be expressed as a percentage of the estimate. This is known as the relative standard error (RSE). The RSE is determined by dividing the standard error of an estimate SE(x) by the estimate x and expressing it as a percentage. That is:
EQUATION  RSE(x) = 100 SE(x) / x
(where x is the estimate).
The relative standard error is a measure of the error likely to have occurred due to sampling.
10. Proportions and percentages formed from the ratio of two estimates are also subject to sampling error. The size of the error depends on the accuracy of both the numerator and the denominator. The formula for the relative standard error of a proportion or percentage is:
EQUATION  RSE (x/y) = square root of [RSE(x)] squared  [RSE(y)] squared
11. Only estimates with a RSE 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 2003
Size of Estimate
 Standard Error
 Relative Standard Error

households  no.  % 
  
1,000  685  68.5 
1,500  865  57.6 
2,000  1,017  50.8 
2,500  1,150  46.0 
3,000  1,271  42.4 
3,500  1,381  39.5 
4,000  1,483  37.1 
5,000  1,669  33.4 
8,000  2,126  26.6 
10,000  2,379  23.8 
20,000  3,333  16.7 
30,000  4,026  13.4 
50,000  5,066  10.1 
100,000  6,814  6.8 
200,000  9,006  4.5 
300,000  10,517  3.5 
500,000  12,676  2.5 
1,000,000  16,086  1.6 
2,000,000  20,059  1.0 

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