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TECHNICAL NOTE DATA QUALITY
3 RSEs for Pregnancy and Employment Transitions of women estimates have been calculated using the Jackknife method of variance estimation. This process 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. However, RSEs for all these estimates are available free-of-charge on the ABS web site <www.abs.gov.au>, released in spreadsheet format as an attachment to this publication, Pregnancy and Employment Transitions, Australia (cat. no. 4913.0). As a guide, the population estimates and RSEs for selected data from table 1 and 2 are presented at tables T1 and table T2 in this Technical Note.
5 In the tables in this publication, only estimates (numbers, percentages and means) 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. *4.6) 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 that they are considered too unreliable for general use.
CALCULATION OF STANDARD ERROR AND RELATIVE STANDARD ERROR
6 RSEs are routinely presented as the measure of sampling error in this publication and related products. SEs can be calculated using the estimates (counts or means) and the corresponding RSEs.
7 An example of the calculation of the SE from an RSE follows. T1 shows that the estimated number of married women aged 35-39 years with a child under two years was 103,300, and the RSE for this estimate is 5.5%. The SE is:
= (RSE / 100) x estimate
= 0.055 x 103,300
= 5,700 (rounded to the nearest 100)
8 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 within the range 97,600 to 109,000 and about 19 chances in 20 that the value will fall within the range 91,900 to 114,700. This example is illustrated in the following diagram:
PROPORTIONS AND PERCENTAGES
9 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 RSEs of proportions not provided in the spreadsheets is given below. This formula is only valid when x is a subset of y.
10 Considering table T1, of the 523,300 women with a child under two years by social marital status, 63,700 or 12.2% stated they were not currently married. The RSE of 63,700 is 9.2% and the RSE for 523,300 is 3.2%. Applying the above formula, the RSE for the proportion of females who were not currently married at the time is:
11 Therefore, from paragraph 7 the SE for the proportion of women with a child under two years who were not married is 1.04 percentage points (12.2/100) x 8.6). Therefore, there are about two chances in three that the proportion of women with a child under two years that were not married is between 11.2% and 13.2%, and 19 chances in 20 that the proportion is within the range 10.2% to 14.2%.
SUMS OR DIFFERENCES BETWEEN ESTIMATES
12 Published estimates may also be used to calculate the sum of, or difference between, two survey estimates (of numbers, means or percentages) where these are not provided in the spreadsheets. Such estimates are also subject to sampling error.
13 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 The sampling error of the sum of two estimates is calculated in a similar way. An approximate SE of the sum of two estimates (x + y) may be calculated by the following formula:
15 An example for the sum of two estimates follows. From paragraph 7 the estimated number of married women with a child under two years aged 35-39 years was 103,300 and the SE is 5,700. From table T1, the estimate of married women aged 40 years and over was 42,200, and the SE is 4,200. The estimate of married women aged 35 years and over is:
16 The SE of the estimate of married women aged 35 years and over is:
17 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 within the range 141,600 to 149,400 and about 19 chances in 20 that the value will fall within the range 137,700 to 153,300.
18 While these formulae will only be exact for sums of, or differences between, separate and uncorrelated characteristics or subpopulations, it is expected to provide a good approximation for all sums or differences likely to be of interest in this publication.
19 A statistical significance test for any comparisons between estimates can be performed to determine whether it is likely that there is a difference between two corresponding population characteristics. The standard error of the difference between two corresponding estimates (x and y) can be calculated using the formula in paragraph 11. This standard error is then used to calculate the following test statistic:
20 If the value of this test statistic is greater than 1.96 then there is evidence, with a 95% level of confidence, of a statistically significant 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 with respect to that characteristic.
21 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.
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