The Central Statistical Office (CSO), Botswana and Statistics South Africa conduct
large scale nationwide surveys on a regular basis. Both the organizations very often use
the same survey design recommended by the UNDP. The survey design involves
selection of first stage units (fsu’s) with inclusion probability proportional to size (IPPS)
sampling design introduced by Goodman and Kish (1950) and the second stage units
(ssu’s) by systematic sampling scheme. CSO, Botswana employed the same sampling
design for “Household Income and Expenditure Survey 2002/03 (HIES, 2002/03)” and
“Botswana Aids Impact Survey II, 2004 (BAIS II, 2004)”. Chaudhuri and Arnab (1982)
proved that for the sampling design recommended by UNDP, the variance of the
population total or mean cannot be estimated unbiasedly. Unbiased variance estimation is
required for estimating precision of the survey estimates, confidence interval, optimum
sample size and testing of hypothesis amongst others. The optimum sample size is the
key factor of determination of cost of a survey and precisions of estimates. CSO used
design factor 2.0 for determination of sample size which was calculated from the
“Household Income and Expenditure Survey, 1993/94 (HIES 1993/94). In our present
investigation we have proposed a few alternative sampling designs to overcome the
problems of variance estimation. The performances of the estimators are tested with the
live data collected by CSO for HIES survey with six indicators. The investigation reveals
that the design effect assumed by CSO is very high. It actually varies between 0.85 to
1.31 for all the six indictors of the existing (CSO) and proposed alternative designs.
Neither the CSO design nor the proposed alternatives is found suitable for all the
indicators. Hence for the consideration of variance estimation one should employ RaoHartley-Cochran
(RHC) or Simple random sampling without replacement (SRSWOR) for
the selection of first stage units and SRSWOR for the selection of second stage units.