CHI-SQUARE TESTS FOR COMPLEX SURVEY DESIGNS: A CASE STUDY OF BOTSWANA AIDS IMPACT SURVEY III

The traditional Pearsonian chi-square tests for goodness of fit, independence and homogeneity are valid when the sample size is large and the sample is selected using the simple random sampling with replacement (SRSWR) method. These tests however are not valid for complex survey designs, such as those for example which involve stratification, clustering and varying probability sampling designs. The standard statistical packages SPSS, BMDP and SAS provide chi-square statistics where it is assumed that the sample is selected by SRSWR methods and hence very often provide inaccurate results. In this article we present more appropriate methods of chi-square test procedures for complex survey designs. Some numerical illustrations are provided using BAIS III survey data which is based on a complex survey design. The results show that the traditional chi-square statistics provide higher values in most of the cases, while improved Rao-Scott adjustments produce lower values for the test statistics. In many cases different conclusions are reached, depending on which of the traditional or improved chi-square statistic are employed.