The estimation of sample size in multi-stage sampling and its application in medical survey

In this paper, methods of deducing the minimum value and the Cauchy–Schwarz inequality were applied to deduce the formulae for the optimum sample sizes for two-stage, two-stage cluster and three-stage sampling, so as to minimize the cost for specified values of the sampling errors and to minimize the sampling errors for specified cost. These formulae were applied successfully in the tuberculosis epidemic survey in Jiangsu Province in China and in the survey of medical cost in Ministry of Railway of China.