TECHNICAL NOTE DATA QUALITY
INTRODUCTION
1 Since the estimates in this publication are based on information obtained from occupants of a sample of dwellings, they are subject to sampling variability. That is, they may differ from those estimates that would have been produced if all dwellings had been included in the survey. One measure of the likely difference is given by the standard error (SE), which indicates the extent to which an estimate might have varied by chance because only a sample of dwellings (or occupants) was included. There are about two chances in three (67%) that a sample estimate will differ by less than one SE from the number that would have been obtained if all dwellings had been included, and about 19 chances in 20 (95%) that the difference will be less than two SEs.
2 Another measure of the likely difference is the relative standard error (RSE), which is obtained by expressing the SE as a percentage of the estimate:
3 RSEs for estimates from the Labour Force and Other Characteristics of Recent Migrants Survey are published for the first time in 'direct' form. Previously a statistical model was produced that related the size of estimates to their corresponding RSEs, and this information was displayed via an 'SE table'. From this point onwards, RSEs for the Labour Force and Other Characteristics of Recent Migrants Survey are calculated for each separate estimate and published individually. The Jackknife method of variance estimation is used for this process, which involves the calculation of 30 'replicate' estimates based on 30 different subsamples of the original sample. The variability of estimates obtained from these subsamples is used to estimate the sample variability surrounding the main estimate.
4 Limited publication space does not allow for the separate indication of the SEs and/or RSEs of all the estimates in this publication, only RSEs for Table 1 have been included at the end of these Technical Notes. However, RSEs for all tables are available free-of-charge on the ABS website <www.abs.gov.au>. released in spreadsheet format as an attachment to this publication, Labour Force and Other Characteristics of Recent Migrants, Australia, November 2007 (cat. no. 6250.0).
5 In the tables in this publication, only estimates (numbers, percentages, means and medians) with RSEs less than 25% are considered sufficiently reliable for most purposes. However, estimates with larger RSEs have been included and are preceded by an asterisk (e.g. *3.4) to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs greater than 50% are preceded by a double asterisk (e.g. **2.1) to indicate they are considered too unreliable for general use.
CALCULATION OF STANDARD ERRORS
6 SEs can be calculated using the estimates (count or means) and the corresponding RSEs. For example, Table 1 shows the estimated number of persons who were recent migrants is 647,000. The RSE table for Table 1, with the RSEs corresponding to the estimates in Table 1, is included at the end of these Technical Notes. This shows the RSE for the estimate is 3.3%. The SE is:
7 Therefore there are about two chances in three that the value that would have been produced if all dwellings had been included in the survey will fall in the range 625,600 to 668,400 and about 19 chances in 20 that the value will fall within the range 604,200 to 689,800. This example is illustrated below.
8 Proportions and percentages formed from the ratio of two estimates are also subject to sampling errors. The size of the error depends on the accuracy of both the numerator and the denominator. A formula to approximate the RSE of a proportion is given below. This formula is only valid when x is a subset of y.
9 For example in Table 1, the estimate for the total number of persons who were recent migrants is 647,000. The estimated number of males who were recent migrants is 299,300, so of all persons who were recent migrants, the proportion who were males is (299,300 / 647,000)*100 or 46.3%.
10 From the RSE table for Table 1, included at the end of these Technical Notes, the RSE of the total number of persons who were recent migrants is 3.3% and the RSE of the number of males who were recent migrants is 4.1%. Applying the above formula, the RSE of the proportion is
11 This then gives an SE of the percentage (46.3%) of (2.4/100)*46.3 = 1.1 percentage points.
12 Therefore there are about two chances in three that the proportion of recent migrants who were males is between 45.2% and 47.4% and 19 chances in 20 that the proportion is within the ranges 44.1% and 48.5%.
DIFFERENCES
13 Published estimates may also be used to calculate the difference between two survey estimates (of numbers or percentages). Such an estimate is subject to sampling error. The sampling error of the difference between two estimates depends on their SEs and the relationship (correlation) between them. An approximate SE of the difference between two estimates (x-y) may be calculated by the following formula:
14 While this formula will only be exact for differences between separate and uncorrelated characteristics or subpopulations, it is expected to provide a good approximation for all differences likely to be of interest in this publication.
SIGNIFICANCE TESTING
15 The statistical significance test for any of the comparisons between estimates was performed to determine whether it is likely that there is a difference between the corresponding population characteristics. The standard error of the difference between two corresponding estimates (x and y) can be calculated using the formula in paragraph 13. This standard error is then used to calculate the following test statistic:
16 If the value of this test statistic is greater than 1.96 then there is good evidence of a real difference in the two populations with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a real difference between the populations.
17 The imprecision due to sampling variability, which is measured by the SE, should not be confused with inaccuracies that may occur because of imperfections in reporting by respondents and recording by interviewers, and errors made in coding and processing data. Inaccuracies of this kind are referred to as non-sampling error, and they occur in any enumeration, whether it be a full count or sample. Every effort is made to reduce non-sampling error to a minimum by careful design of questionnaires, intensive training and supervision of interviewers, and efficient operating procedures.
RELATIVE STANDARD ERROR
18 Relative Standard Errors for Table 1 are included below. However, RSEs for all tables are available free-of-charge on the ABS website <
www.abs.gov.au>, released in spreadsheet format as an attachment to this publication.
TABLE 1 RSEs: ALL PERSONS AGED 15 YEARS AND OVER, Migration status as at November 2007 - By sex |
| |
| | | | | Males | Females | Persons | Proportion of all persons | |
| | | | | % | % | % | % | |
| |
Born in Australia | 0.5 | 0.5 | 0.4 | 0.4 | |
Born overseas | 1.4 | 1.3 | 1.2 | 1.2 | |
| Arrived before 1998 | 1.2 | 1.5 | 1.2 | 1.2 | |
| Arrived after 1997 | 3.3 | 2.8 | 2.7 | 2.7 | |
| | Aged less than 15 years on arrival | 12.3 | 11.3 | 9.0 | 9.0 | |
| | Aged 15 years and over on arrival | 3.1 | 2.8 | 2.6 | 2.6 | |
| | | Recent migrants and temporary residents | 3.7 | 2.9 | 2.7 | 2.7 | |
| | | | Recent migrant | 4.1 | 3.5 | 3.3 | 3.3 | |
| | | | Temporary resident | 7.2 | 7.3 | 6.5 | 6.5 | |
| | | | Status not determined | 58.9 | 49.8 | 51.2 | 51.2 | |
| | | Australian/New Zealand citizen before arrival, currently holds New Zealand citizenship or born in New Zealand | 7.7 | 7.8 | 7.3 | 7.3 | |
| | | Planning to stay less than 12 months | 36.0 | 28.9 | 25.5 | 25.5 | |
Total | 0.2 | 0.3 | 0.3 | 0.3 | |
| |