Effect of number and sampling fraction of primary sampling unit on sampling error approximation and statistical inference

Objective To examine how number and sampling fraction of primary sampling unit (PSU) affect sampling error estimation and statistical inference with approximation method.Methods We used systolic blood pressure measurements of 98 587 respondents from the 2010 China Chronic Disease and Risk Factor Surveillance Survey as study population to conduct a two-stage sampling simulation.We adopted Taylor's series linearization to estimate sampling error of mean and 95%confidence interval (95%CI),with or without finite population correction (FPC).For each design,the estimated sampling error was compared with the true sampling error,and the probability that population mean covered by 95%CI was determined.Results Sampling error declined rapidly from 4.13 mm Hg to 1.91 mm Hg by 53.8%while the number of PSU increased from 2 to 10,but declined mildly if number of PSU was getting more than 20.With consideration of FPC,probability of estimated 95%CIs covering the parameter fluctuated with increase of PSU sampling fraction:when sampling fraction<30%,the probability of 95%CIs covering the parameter was around 94.0%;when sampling fraction increased to>30%,the probability of 95%CIs covering the parameter decreased to 88.2%,leading to a sensitive statistical inference.In the situation of without FPC,the probability of 95%CIs covering the parameter was higher than that estimation with FPC.The probability of 95%CIs covering the parameter went up when PSU sampling fraction increased to>20%,leading to a conservative statistical inference.Conclusion Number of PSU should be determined with acceptable variation of the estimates and feasibility of the survey.Caution should be exercised when estimating sampling error using approximation method with considerable sampling fraction of PSU.