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# Stratified Random Sampling

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❶July Learn how and when to remove this template message. The precision of this design is highly dependent on the sampling fraction allocation of the researcher.

## Stratified random sampling   It can produce a weighted mean that has less variability than the arithmetic mean of a simple random sample of the population. In computational statistics , stratified sampling is a method of variance reduction when Monte Carlo methods are used to estimate population statistics from a known population. Assume that we need to estimate average number of votes for each candidate in an election.

Assume that country has 3 towns: Town A has 1 million factory workers, Town B has 2 million office workers and Town C has 3 million retirees. We can choose to get a random sample of size 60 over the entire population but there is some chance that the random sample turns out to be not well balanced across these towns and hence is biased causing a significant error in estimation.

Instead if we choose to take a random sample of 10, 20 and 30 from Town A, B and C respectively then we can produce a smaller error in estimation for the same total size of sample. A real-world example of using stratified sampling would be for a political survey. 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.

A stratified survey could thus claim to be more representative of the population than a survey of simple random sampling or systematic sampling. The reasons to use stratified sampling rather than simple random sampling include . 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. Stratified sampling is not useful when the population cannot be exhaustively partitioned into disjoint subgroups. It would be a misapplication of the technique to make subgroups' sample sizes proportional to the amount of data available from the subgroups, rather than scaling sample sizes to subgroup sizes or to their variances, if known to vary significantly -- e.

Data representing each subgroup are taken to be of equal importance if suspected variation among them warrants stratified sampling. If subgroup variances differ significantly and the data needs to be stratified by variance, it is not possible to simultaneously make each subgroup sample size proportional to subgroup size within the total population.

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 deleterious effect on the performance of any analysis on the dataset, e. Combining sub-strata to ensure adequate numbers can lead to Simpson's paradox , where trends that actually exist in different groups of data disappear or even reverse when the groups are combined.

The mean and standard error of stratified random sampling are given by: Foregoing the finite population correction gives:. For proportional allocation strategy, the size of the sample in each stratum is taken in proportion to the size of the stratum.

Suppose that in a company there are the following staff: Another easy way without having to calculate the percentage is to multiply each group size by the sample size and divide by the total population size size of entire staff:. From Wikipedia, the free encyclopedia. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources.

Unsourced material may be challenged and removed. July Learn how and when to remove this template message. In a proportionate stratified method, the sample size of each stratum is proportionate to the population size of the stratum. For example, if the researcher wanted a sample of 50, using age range, the proportionate stratified random sample will be obtained using this formula: Assuming a population size of , MBA grads per year,.

Same method is used for the other age range groups. Now that the strata sample size is known, the researcher can perform simple random sampling in each stratum to select his survey participants. In other words, 25, grads from the age group will be selected randomly from the entire population, 16, grads form the age range will be selected from the population randomly, and so on.

In a disproportional stratified sample, the size of each stratum is not proportional to its size in the population. It is important to note that one person cannot fit into multiple strata. Each entity must only fit in one stratum. Having overlapping subgroups means that some individuals will have higher chances of being selected for the survey, which completely negates the concept of stratified sampling as a type of probability sampling.

The main advantage of stratified sampling is that it captures key population characteristics in the sample. Similar to a weighted average, this method of sampling produces characteristics in the sample that are proportional to the overall population. Stratified sampling works well for populations with a variety of attributes, but is otherwise ineffective if subgroups cannot be formed.

Stratification gives a smaller error in estimation and greater precision than the simple random sampling method. The greater the differences between the strata, the greater the gain in precision. A sampling distribution is a probability distribution of a statistic The central limit theorem states that when one aggregates samples A T distribution is a type of probability function that is appropriate Learn more about the convenience of the subscription beauty box industry, and discover why the Birchbox company in particular has become so popular.

This phenomenon can cause a trader to abandon a proven strategy or risk everything on chance. Use these calculations to uncover the risk involved in your investments. Learn how Vanguard index funds work. See how the index sampling technique allows Vanguard to charge low expense ratios that can save investors money. Are the markets random or cyclical? Depends on whom you ask. ## Main Topics

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Stratified sampling is a probability sampling method and a form of random sampling in which the population is divided into two or more groups (strata) according to one or more common attributes. Stratified random sampling intends to guarantee that the sample represents specific sub-groups or strata.

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Stratified sampling is a probability sampling technique wherein the researcher divides the entire population into different subgroups or strata, then randomly selects the final subjects proportionally from the different strata.

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Stratified random sampling is a method of sampling that involves the division of a population into smaller groups known as strata. In stratified random sampling or stratification, the strata are formed based on members' shared attributes or . “According to Webster (), to research is to search or investigate exhaustively. It is a careful or diligent search, studious inquiry or examination especially investigation or experimentation aimed at the discovery and interpretation of facts, revision of accepted theories or laws in the light.

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Stratified random sampling. Stratified random sampling is a type of probability sampling technique [see our article Probability sampling if you . Stratified random sampling is a type of probability sampling using which a research organization can branch off the entire population into multiple non-overlapping, homogeneous groups (strata) and randomly choose final members from the various strata for research which reduces cost and improves.