Australian Bureau of Statistics
Relative Standard Error
Sources of Variability
RSEs of proportions and percentages
Proportions and percentages formed from the ratio of two estimates are also subject to sampling errors. The size of the error depends of the accuracy of both the numerator and denominator. A formula to approximate the RSE of a proportion is given below:
Note - this formula only holds when the x is a subset of y. It should not be used if this is not the case i.e. estimates of 'rates' as opposed to proportions.
SEs may also be used to calculate SEs for the difference between two survey estimates (numbers or percentages). The sampling error of the difference between the two estimates depends on their individual 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:
SE(x-y) =sqrt[SE(x)]2 +[SE(y)]2
While this formula will only be exact for differences between separate and uncorrelated characteristics of subpopulations, it is expected to provide a reasonable approximation for most differences likely to be of interest in relation to this survey.
Note that it is the RSE of a percentage that is displayed, from which the SE may be calculated. For example if the estimated proportion is 30% with an RSE of 20%, then the SE for the proportion is 6%.
In some cases, the formula for the approximation of the RSE of a proportion may be unsuitable to use because the RSE of the numerator is very close to, or below, the RSE of the denominator. In this case the RSE will be suppressed. It is recommended to use the RSE of the numerator as a proxy for the RSE of the proportion in the event of this occurrence.
Standard Errors of Means and Sums
The estimates of means and sums of continuous variables are subject to sampling variability and random adjustment. As for population estimates, the variability due to sampling and random adjustment is combined into the calculated Standard Error, and the Relative Standard Error is reported. The component of variability arising from sampling is calculated using the Jackknife method.
Standard Errors of Quantiles
The estimates of quantiles such as medians, quartiles, quintiles and deciles are subject to sampling variability and random adjustment. As for population estimates, the variability due to sampling and random adjustment is combined into the calculated Standard Error, and the Relative Standard Error is reported. The component of variability arising from sampling is calculated using the Woodruff method. This is also true for Equal Distribution Quantiles.
Reliability of Estimates
Estimates with RSEs of 25% or more are not considered reliable for most purposes. Estimates with RSEs greater than 25% but less than or equal to 50% are annotated by an asterisk to indicate they are subject to high SEs and should be used with caution. Estimates with RSEs greater than 50% have their RSE suppressed in order to prevent the release of confidential data, and are annotated by a double asterisk. These estimates are considered too unreliable for general use.
The imprecision due to sampling variability and random adjustment 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 may occur in any enumeration, whether it be a full count or a 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.
This page first published 27 September 2011, last updated 24 January 2013