Thesis (M.Sc. (Statistics)) -- University of Limpopo, 2019 / This research study has demonstrated the complexity involved in complex survey sample design (CSSD). Furthermore the study has proposed methods to account for each step taken in sampling and at the estimation stage using the theory of survey sampling, CSSD-based case studies and practical implementation based on census attributes. CSSD methods are designed to improve statistical efficiency, reduce costs and improve precision for sub-group analyses relative to simple random sample(SRS).They are commonly used by statistical agencies as well as development and aid organisations. CSSDs provide one of the most challenging fields for applying a statistical methodology. Researchers encounter a vast diversity of unique practical problems in the course of studying populations. These include, interalia: non-sampling errors,specific population structures,contaminated distributions of study variables,non-satisfactory sample sizes, incorporation of the auxiliary information available on many levels, simultaneous estimation of characteristics in various sub-populations, integration of data from many waves or phases of the survey and incompletely specified sampling procedures accompanying published data. While the study has not exhausted all the available real-life scenarios, it has outlined potential problems illustrated using examples and suggested appropriate approaches at each stage. Dealing with the attributes of CSSDs mentioned above brings about the need for formulating sophisticated statistical procedures dedicated to specific conditions of a sample survey. CSSD methodologies give birth to a wide variety of approaches, methodologies and procedures of borrowing the strength from virtually all branches of statistics. The application of various statistical methods from sample design to weighting and estimation ensures that the optimal estimates of a population and various domains are obtained from the sample data.CSSDs are probability sampling methodologies from which inferences are drawn about the population. The methods used in the process of producing estimates include adjustment for unequal probability of selection (resulting from stratification, clustering and probability proportional to size (PPS), non-response adjustments and benchmarking to auxiliary totals. When estimates of survey totals, means and proportions are computed using various methods, results do not differ. The latter applies when estimates are calculated for planned domains that are taken into account in sample design and benchmarking. In contrast, when the measures of precision such as standard errors and coefficient of variation are produced, they yield different results depending on the extent to which the design information is incorporated during estimation. The literature has revealed that most statistical computer packages assume SRS design in estimating variances. The replication method was used to calculate measures of precision which take into account all the sampling parameters and weighting adjustments computed in the CSSD process. The creation of replicate weights and estimation of variances were done using WesVar, astatistical computer package capable of producing statistical inference from data collected through CSSD methods. Keywords: Complex sampling, Survey design, Probability sampling, Probability proportional to size, Stratification, Area sampling, Cluster sampling.

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