# Stratified sampling

Stratified sampling is a method of sampling from a population in statistics.

When sub-populations vary considerably, it is advantageous to sample each subpopulation (stratum) independently. Stratification is the process of grouping members of the population into relatively homogeneous subgroups before sampling. The strata should be mutually exclusive : every element in the population must be assigned to only one stratum. The strata should also be collectively exhaustive : no population element can be excluded. Then random sampling is applied within each stratum. This often improves the representativeness of the sample by reducing sampling error. It can produce a weighted mean that has less variability than the arithmetic mean of a simple random sample of the population.

There are several possible strategies:

1. Proportionate allocation uses a sampling fraction in each of the strata that is proportional to that of the total population. If the population consist of 60% in the male stratum and 40% in the female stratum, then the relative size of the two samples (one males, one females) should reflect this proportion.
2. Optimum allocation (or Disproportionate allocation) - Each stratum is proportionate to the standard deviation of the distribution of the variable. Larger samples are taken in the strata with the greatest variability to generate the least possible sampling variance.

A real-world example of using stratified sampling would be for a US political survey. If we wanted the respondents to reflect the diversity of the population of the United States, 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. A stratified survey could thus claim to be more representative of the US population than a survey of random sampling or systematic sampling.

• focuses on important subpopulations but ignores irrelevant ones
• improves the accuracy of estimation
• efficient
• sampling equal numbers from strata varying widely in size may be used equate the statistical power of tests of differences between strata.

• can be difficult to select relevant stratification variables
• not useful when there are no homogeneous subgroups
• can be expensive
• requires accurate information about the population.

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