Stratified sampling

Stratification is the process of dividing members of the population into homogeneous subgroups before sampling.

That is, it should be collectively exhaustive and mutually exclusive: every element in the population must be assigned to one and only one stratum.

[1] Assume that we need to estimate the average number of votes for each candidate in an election.

We can choose to get a random sample of size 60 over the entire population but there is some chance that the resulting random sample is poorly balanced across these towns and hence is biased, causing a significant error in estimation (when the outcome of interest has a different distribution, in terms of the parameter of interest, between the towns).

If the respondents needed to reflect the diversity of the population, the researcher would specifically seek to include participants of various minority groups such as race or religion, based on their proportionality to the total population as mentioned above.

The reasons to use stratified sampling rather than simple random sampling include[2] If the population density varies greatly within a region, stratified sampling will ensure that estimates can be made with equal accuracy in different parts of the region, and that comparisons of sub-regions can be made with equal statistical power.

For example, in Ontario a survey taken throughout the province might use a larger sampling fraction in the less populated north, since the disparity in population between north and south is so great that a sampling fraction based on the provincial sample as a whole might result in the collection of only a handful of data from the north.

Data representing each subgroup are taken to be of equal importance if suspected variation among them warrants stratified sampling.

For an efficient way to partition sampling resources among groups that vary in their means, variance and costs, see "optimum allocation".

The problem of stratified sampling in the case of unknown class priors (ratio of subpopulations in the entire population) can have a deleterious effect on the performance of any analysis on the dataset, e.g.

[3] In that regard, minimax sampling ratio can be used to make the dataset robust with respect to uncertainty in the underlying data generating process.

[3] Combining sub-strata to ensure adequate numbers can lead to Simpson's paradox, where trends that exist in different groups of data disappear or even reverse when the groups are combined.

The mean and variance of stratified random sampling are given by:[2] where Note that the term