Grouping of individuals

A simple random sample of individuals from some population is conceptually the easiest sampling scheme. However more accurate estimates of population characteristics can often be obtained with different sampling schemes.

Weekly turnover of grocery stores

In practice, the aim is more likely to be estimation of the total grocery turnover in the city, but this is simply 100 times the mean turnover, so stratified sampling gives the same improvement over a simple random sample.

Groups with different variability (advanced)

In stratified random samples, random samples are usually taken from the different strata in proportion to the number of population values in the strata, but this proportionality is not essential. Greater accuracy can be obtained by selecting larger samples from strata with greater variability.

However if sample size is not proportional to stratum size, the overall sample mean is no longer appropriate for estimating the overall population mean. If there are k strata of size N1, N2, ..., Nk, and samples of size n1, n2, ..., nk are taken from the strata, giving means 1, 2, ..., k , then the population mean should be estimated by

Weekly turnover by grocery stores

An extreme example of disproportionate sample sizes occurs when using sampling to estimate the mean or total profits of companies. If a list of 'large' companies is available, it is often best to record information from all of the large companies but only sample a small fraction of the smaller companies.