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INTERPRETATION OF RESULTS
For a number of GSS data items, some respondents were unwilling or unable to provide the required information. No imputation was undertaken for this missing information. Where responses for a particular data item were missing for a person or household they were recorded in a 'not known' or 'not stated' category for that data item. These 'not known' or 'not stated' categories are not shown in the publication tables. However, the person or household has been included in the total for most data items. The exception is the equalised gross household income data item where it was more appropriate to calculate percentages excluding the missing values. Below is a table showing the number and proportion of missing values for key GSS data items.
Comparison of estimates
Published estimates may also be used to calculate the difference between two survey estimates. 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:
While the above formula will be exact only for differences between separate and uncorrelated (unrelated) characteristics of sub-populations, it is expected that it will provide a reasonable approximation for all differences likely to be of interest in this publication.
For 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. This is done by calculating the standard error of the difference between two estimates (x and y) and using that to calculate the test statistic using the following formula:
If the value of the test statistic is greater than 1.96 then we may say there is good evidence of a statistically significant difference between the two populations with respect to that characteristic. Otherwise, it cannot be stated with confidence that there is a real difference between the populations.
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.
Calculating standard errors for 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 on the accuracy of both the numerator and the denominator. For proportions where the denominator is an estimate of the number of persons in a group and the numerator is the number of persons in a sub-group of the denominator group, the formula to approximate the RSE is given by:
The estimates from the 2010 GSS are based on information collected from August to November 2010, and due to seasonal effects they may not be fully representative of other time periods in the year. For example, the GSS asked standard ABS questions on labour force status to determine whether a person was employed. Employment is subject to seasonal variation throughout the year. Therefore, the GSS results for employment could have differed if the GSS had been conducted over the whole year or in a different part of the year.