Complex surveys are surveys which involve a survey design other than simple random sampling. In practice sample surveys require a complex design due to many factors such as cost, time and the nature of the population. Standard statistical methods such as linear regression, contingency tables and multivariate analyses are based on data which are independently and identically distributed (IID). That is, the data is assumed to have been selected by a simple random sampling design. The assumptions underlying standard statistical methods are generally not met when the data is from a complex design. A measure of the efficiency of a design was found by the ratio of the variance of the actual design over the variance of a simple random sample (of the same sample size). This is known as the design effect (deff). There are two forms of design effects; one proposed by Kish (1965) and another termed the misspecification effect (meff) by Skinner et al. (1989). Throughout the thesis, the design effect referred to is Skinner et al. (1989)'s misspecification effect. Cluster sampling generally yields a deff greater than one and stratified samples yields a deff less than one. Some researchers have adopted a model based approach for parameter estimation rather than the traditional design based approach. The model based approach is one which each possible respondent has a distribution of possible values, often leading to the equivalent of an infinite background population, called the superpopulation. Both approaches are discussed throughout the thesis. Most of the standard computing packages available have been developed for simple random sample data. Specialized packages are needed to analyse complex survey data correctly. PC CARP and SUDAAN are two such packages. Three examples of statistical analyses on complex sample surveys were explored using the specialized statistical packages. The output from these packages were compared to a standard statistical package, The SAS System. It was found that although SAS produced the correct estimates, the standard errors were much smaller than those from SUDAAN. This led, in regression for example, to a much higher number of variables appearing to be significant when they were not. The examples illustrated the consequences of using a standard statistical package on complex data. Statisticians have long argued the need for appropriate statistics for complex surveys.