|Page tools: Print Page Print All RSS Search this Product|
5 One measure of the likely difference in estimates is given by the Standard Error (SE), which indicates the extent to which an estimate might have varied because only a sample of dwellings was included. There are about two chances in three (67%) that the sample estimate will differ by less than one SE from the figure that would have been obtained if all dwellings had been included, and about 19 chances in 20 that the difference will be less than two SEs.
6 For estimates of population sizes, the size of the SE generally increases with the level of the estimate, so that the larger the estimate, the larger the SE. However, the larger the sampling estimate the smaller the SE becomes in percentage terms. Thus, larger sample estimates will be relatively more reliable than smaller estimates. SE can be calculated using the estimates (counts or percentages) and the corresponding Relative Standard Error (RSE). For example, in this publication the estimated males aged 18 years and over who experienced physical assault in the last 12 months was 309,400. The RSE corresponding to this estimate is 8.7%. The SE is calculated by:
= (8.7 / 100) * 309400
= 26,900 (rounded to the nearest 100)
7 The RSE is obtained by expressing the SE as a percentage of the estimate to which it related. The RSE is a useful measure in that it provides an immediate indication of the percentage errors likely to have occurred due to sampling, and thus avoids the need to refer also to the size of the estimate.
8 Estimates with RSEs less than 25% are considered sufficiently reliable for most purposes. However, estimates with RSEs of 25% or more are included in this publication of results and have been appropriately identified to use with caution. RSEs are presented in the tables of the publication for estimates ('000). Estimates with RSEs greater than 25% but less than or equal to 50% are annotated with an asterisk (*) to indicate they are subject to high SEs relative to the size of the estimate and should be used with caution. Estimates with RSEs of greater than 50%, annotated with a double asterisk (**), are considered too unreliable for most purposes. These estimates can be aggregated with other estimates to reduce the overall sampling error. Note that RSEs for proportion estimates (%) are not presented in the tables of this publication, but rather the Margin of Error (MoE) is presented (see section below). However RSEs can be produced from the TableBuilder or Detailed Microdata products or by request.
Calculation of Margin of Error
9 Another useful measure is the Margin of Error (MoE), which describes the distance from the population value that the sample estimate is likely to be within, and is specified at a given level of confidence. Confidence levels typically used are 90%, 95% and 99%. For example, at the 95% confidence level, the MoE indicates that there are about 19 chances in 20 that the estimate will differ by less than the specified MoE from the population value (the figure obtained if all dwellings had been enumerated). The MoE at the 95% confidence level is expressed as 1.96 times the SE.
10 A confidence interval expresses the sampling error as a range in which the population value is expected to lie at a given level of confidence. The confidence interval can easily be constructed from the MoE of the same level of confidence, by taking the estimate plus or minus the MoE of the estimate. In other terms, the 95% confidence interval is the estimate +/- MoE i.e. the range from minus 1.96 times the SE to the estimate plus 1.96 times the SE. The 95% MoE can also be calculated from the RSE by the following, where y is the value of the estimate:
11 Note due to rounding, the SE calculated from the RSE may be slightly different to the SE calculated from the MoE for the same estimate. The SE of estimate using MoEs is calculated by:
12 Using the two formulas above, it was found that there are about 19 chances in 20 that the estimate of the proportion of females aged 18 years and over who experienced sexual harassment in the last 12 months (17.3%) is within +/- 1.1 percentage points from the population value. Similarly, there are about 19 chances in 20 that the proportion of females aged 18 years and over who experienced sexual harassment in the last 12 months is within the confidence interval of 16.2% to 18.4%.
13 In the tables in this publication, MoEs are presented for the proportion estimates (%). Proportion estimates are preceded by a hash (e.g. #10.2) if the corresponding MoE is greater than 10 percentage points. An estimate is also preceded by a hash if the MoE is large enough such that the corresponding confidence interval for this estimate would exceed the value of 0% and/or 100%; the natural limits of a proportion. The latter situation will occur if the MoE is greater than the estimate itself, or greater than 100 minus the estimate. Users should give the margin of error particular consideration when using this estimate. Note that MoEs for 1996 proportion estimates in the tables for this publication were calculated using the RSEs presented in the RSE tables found in the Women’s Safety Survey, 1996 (cat. no. 4128.0).
Standard error of a difference
14 The difference between two survey estimates is itself an estimate and is therefore subject to sampling error or variability. The sampling error of the difference between the two estimates depends on their individual SEs and the level of statistical association (correlation) between the estimates. An approximate SE of the difference between two estimates (x-y) may be calculated by the following formula:
15 For example, the number of females who have been stalked minus the number of males who have been stalked. While this formula will only be exact for differences between separate sub-populations or uncorrelated characteristics of sub-populations, it is expected to provide a reasonable approximation for most differences likely to be of interest in relation to this survey.
Significance testing on differences between survey estimates
16 When comparing estimates between surveys or between populations within a survey, it is useful to determine whether apparent differences are 'real' differences between the corresponding population characteristics or simply the product of differences between the survey samples. One way to examine this is to determine whether the difference between the estimates is statistically significant. A statistical significance test for a comparison between estimates can be 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 shown above in the Standard error of a difference section. This standard error is then used to calculate the test statistic:
17 If the value of this test statistic is greater than 1.96 then there is good 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 (at the 95% confidence level) that there is a real difference between the populations.
18 Data presented in the commentary chapters of this publication have been significance tested to assess whether or not there is a difference (for example, between men and women) or change (for example between 2012 and 2016). When undertaking additional analysis of data presented in the tables, significance testing is recommended.
Example of estimates where there was a statistically significant difference
19 An estimated 5.4% of all men aged 18 years or over and 3.5% of all women aged 18 years or over had experienced physical violence during the 12 months prior to the survey.
20 For information on detailed reliability of estimates, refer to the Data Quality and Technical Notes page in the Personal Safety Survey, Australia: User Guide, 2016 (cat. no. 4906.0.55.003).
These documents will be presented in a new window.