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Estimating sample sizefor a given confidence interval to a proportion
The principle here is exactly the same as for estimating sample size for a given confidence limit for a mean Again it is assumed that you are using random sampling. In this case you only require an estimate of the proportion with the character of interest (that is, the prevalence in the case of a disease). Again the formula for confidence limits is rearranged to estimate the number of samples (n) required for the desired confidence limit. Hence
The same principles apply for estimating sample size for more complex sampling plans using stratification or clustering. However, since the mean and variance of your population are likely to vary (sometimes quite considerably), your estimation of the required sample size will only be an approximation. Hence it is often recommended that the simple formula here is used to give a lower limit to the required sample size, and that figure is increased by 1020 % if more complex designs are used. Worked exampleA survey is being carried out to estimate the prevalence of trypanosomiasis in cattle in a district of Tanzania. It is planned to use simple random sampling for the survey. A preliminary sample of 100 animals gives the proportion infected as 0.32. If we wish to estimate our prevalence ± 5%, the value of L is 0.05.
Hence we would need to take a sample of 334 animals to provide our required level of precision
