Since 2002 information about the health of the New South Wales (NSW) population has been obtained using the NSW Population Health Survey (NSWPHS) . This survey is a continuous sample survey of approximately 15,000 persons each year. The survey is stratified by health administration area and equal numbers are selected from each of the strata, using random digit dialing (RDD) of landline phone numbers and computer assisted telephone interviewing (CATI) with one person from the selected household being randomly selected.
Because of the potential for non-coverage bias from the growing number of mobile-only phone users in the population, estimated to be 19% in Australia in 2011 , mobile phone numbers were included in 2012 using an overlapping dual-frame design. Coverage bias is the product of the proportion of the population not covered and the difference in the mean of the variable of interest between the covered group and the non-covered group . Evidence from the National Health Interview Survey (NHIS) in the US has shown the mobile-only phone users substantial different for the health indicators: five or more drinks in one day at least once in the past year (17.5% v 30.5% - 74% higher), current smokers (14.5% v 24.3% - 68% higher), and ever diagnosed with diabetes (10.8% v 6.2% - 43% lower) .
The landline phone sample procedures were the same as in previous years. The mobile phone sample procedures were as follows; NSW residents were selected using RDD of mobile phone numbers using CATI and the mobile phone owner was selected. If the respondent had one or more children one child was also selected at random in order to ensure that children of people who did not have a landline were also included. Further details about the methodology, call outcomes and representation of the sample in the first quarter of 2012 are provided in Barr et al. , and the questions in the questionnaire are available from the survey website . In the overlapping dual-frame design there are three types of phone use; mobile-only, landline-only and dual-phone users-people with a mobile phone and living in a household with a landline phone—who could now be selected though either the landline or mobile phone number sampling frames.
In the previous landline based samples for the NSWPHS, equal sample sizes were used in each stratum, even though the populations differed substantially and therefore the probability of selection varied by stratum. Moreover, as one person was randomly selected from each selected household, the probability of selection also varied by household size. Weights were calculated for use in survey estimation to account for the differences in probabilities of selection and then benchmarked to the latest NSW population by age group, sex and stratum as shown in Steel  and summarised in Appendix A. The use of equal probabilities to select landline phones in each stratum meant that the factor
, which is the ratio of phone numbers T
in stratum h to the number of phone numbers in the sample t
, cancelled in the previous calculation of the weights, and so the actual number of landline phone numbers in each of the strata did not need to be known. However, with the inclusion of the mobile phone frame this is not the case and the number of landlines and mobile phone numbers in the population for each stratum needed to be estimated. In 2011 the Australian Communication and Media Authority (ACMA) estimated that there were 29.28 million mobile phone numbers and 10.54 million landline phone numbers in Australia . Estimates, however, are not routinely provided by State, let alone by health administration area.
As the previous NSWPHS samples came from a single frame the weighting did not need to account for the differing chances of selection by type of phone use. However, with the inclusion of the mobile phone numbers, using an overlapping dual-frame design, dual-phone users now have an increased chance of selection because they could be selected from either frame. There is currently a growing body of knowledge on issues and methods to deal with overlapping frames as summarised in the American Association for Public Opinion Research (AAPOR): Cell Phone Task Force Report , and in particular the use of composite weights to adjust for the increased chance of selection of dual-phone users. However the most recent detailed description of dual frame weighting available in Australia from the Dual-frame Omnibus Survey conducted in 2012 did not need to deal with disproportionate stratification of the landline frame, data needing to be collected about children as well as adults, and how to apply an overlap adjustment .
Hartley 1962 and 1974 [9, 10] first described the calculation of these composite weights in overlapping frames. We use the notation of A for landline frame, B for the mobile frame, Y for the population total of interest, y for the estimator, a for landline only component, b for mobile only component and ab for dual phone users component. In this case the composite estimator is defined as y
where the estimate for the overlap population is
being the estimators for persons with both mobile and landlines from frame A and B respectively and the composite factor being between 0 and 1 (0 < λ <1). Most overlapping dual frame surveys conducted to date have used a constant composite factor λ and the most common value is 0.5 [11–13]. So with overlapping dual-frames design surveys being relatively new in Australia [5, 8, 14, 15] the use of λ = 0.5 as the compositing factor was considered appropriate.
Calculation of weights, in an overlapping dual-frame design, ideally requires type of phone use benchmarks as well as population benchmarks . In the USA type of phone use benchmarks, at the national level, are collected using the NHIS , where questions on residential phone use have been included since 1963 and mobile phone use since 2003.
Currently there is no equivalent source of information on type of phone use in Australia, although landline phone use from the Australian Health Survey (AHS) conducted by the Australian Bureau of Statistics (ABS), are expected to be available in 2014 . However, landline and mobile phone use questions have been included in the Roy Morgan Single Source Survey (RMSSS) since 2005  for ACMA communication reporting. It was estimated in the 2010–11 report that as at June 2011, 74% of adults in Australia lived in a household with a landline and a mobile phone, 5% lived in a household with a landline but no mobile phone, and 19% lived in a household with only a mobile phone; with the highest mobile-only phone rates being in young adults (37% in 18 to 24 year olds) .
Because weights are used to eliminate bias that would arise from ignoring the differences in selection probabilities and also to improve estimates by adjusting to known population benchmarks, when a design change occurs it is also important to assess how the design effect changes due to weighting, using weighting effects. The design effect is the factor by which the sampling variances are larger (or smaller) than those associated with a simple random sample and no weighting .
This paper describes and details the final weighting strategy adopted to properly combine the data from the two overlapping sample frames in the NSWPHS and the benchmark populations used, based on the limited information available in Australia. We then compare the weight effects for the overlapping dual-frame sampling design to the previous landline frame sampling design.