Household surveys are the most common type of survey used for providing information about the social and economic characteristics of a population of people. In these surveys, information is usually collected by sampling the houses where people live and then enumerating one or more persons at each home. Current sampling methodologies used in designing household surveys generally do not take into account the spatial structure of populations. This may lead to selection of units (i.e., households, individuals) near to each other that usually provide similar information in the sample. As a result, the selected sample tends to be less efficient than a sample that reflects all attributes of the population.

Spatially balanced sampling is a popular design for selecting samples from natural resources and environmental studies, which avoids selecting neighbouring units in the same sample. Spatially balanced sampling design ensures the selection of a representative sample by providing a spatial coverage of a region corresponding to the population of interest.

This doctoral thesis aims to assess the possibility of applying spatially balanced sampling in designing household surveys. After investigating spatially balanced methods available in the literature, balanced acceptance sampling (BAS), developed by Robertson et al (2013) is considered for further investigation in this study.

This research comprises two main parts: (1) exploring the characteristics of BAS from a practical perspective, (2) promoting the application of spatially balanced sampling in household surveys. The first part looks into the advantages of the BAS method in practical cases. It aims to highlight the potential advantages of the BAS method for selecting samples in practical situations in environmental studies. The flexible characteristics of BAS and its practical benefits (e.g., being able to accommodate missed sampling units and the ability to add extra sampling units during survey implementation) discussed in the first part, show that BAS has the potential to be extended for application in other surveys, specifically, household surveys.

In the second part, the applicability of spatially balanced sampling in household surveys is assessed. A technique for selecting a spatially balanced sample from a discrete population, called BAS-Frame, is introduced. The spatial and statistical properties of the proposed method are investigated through conducting simulation studies using the census 2013 meshblocks of selected regions in New Zealand. The results from these simulation studies show that the proposed method is sufficiently robust in spreading the sample over the population of interest. In addition, it is seen that applying spatially balanced sampling in selecting samples for household surveys provides more precise estimates when compared to non-spatially balanced sampling methods.

The feasibility of spatially balanced sampling methods to deal with some practical aspects of designing a household survey is also investigated in the second part (e.g., designing a primary sampling unit (PSU) which meet a pre-specified minimum number of sampling units, designing longitudinal surveys, and selecting a sample in the presence of auxiliary variables). A method on the basis of the BAS-Frame is developed to merge undersized units with their nearby units as much as possible to define PSUs. A simulation study shows that the proposed method is more powerful than the conventional method (i.e., the Kish method) in combining the undersized units with their undersized neighbours. The application of the BAS-Frame for controlling overlap between rotation groups in the longitudinal designs is discussed. Finally the performance of the BAS-Frame in spreading the sample over the space of the auxiliary variables available in the frame is investigated. This study shows that in the case of the existence of a small number of auxiliary variables (fewer than five variables), the BAS- Frame can provide a good spread, not only over the geographical space of the population, but also over the space of the auxiliary variables.

This research, by studying multiple concepts of spatially balanced sampling, leads to better understanding of these sampling methods, and the advantages of extending their applications to household surveys.