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Double sampling is a two-phase method of sampling for an experiment, research project, or inspection. An initial sampling run is followed by preliminary analysis, after which another sample is taken and more analysis is run.

It is used in three main ways: acceptance/rejection double sampling, ratio double sampling, and stratification double sampling. We’ll look at each of them in detail below.

## Acceptance/rejection double sampling.

Used primarily in industrial sampling inspection, this is the most simple type of two phase sampling.

First, an initial random sample is taken and tested for variable x. If a certain high threshold is reached, the result is considered to be positive and no further samples are run. If a certain low threshold is not met, the result is considered to be negative and, again, no further samples are run. But if the results are in some middle ground, a new, larger sample is taken and the results from both runs are used to draw a conclusion.

## Ratio double sampling

In this type of sampling, an auxiliary, easy to study variable x is used to gather information on the harder-to-research target variable y. Variable x is chosen as one which is highly correlated to y.

First, a large random sample is analyzed for x. Then, a subset of this sample is analyzed for y. The ratio of x to y over the subset is taken, and this allows us to reach conclusions as to what the value of y will be in the larger sample (and so in the population as a whole).

## Stratification double sampling.

A two phase sampling method can also be used in situations involving stratification. In this way of sampling, an initial random sample allows us to target the second sample appropriately.

In our initial random sample we look only at the stratification of a population, and the second sample, in which our target variable is studied, is taken over the stratification categories in a representative way.

For example, if you were studying how many books the average city dweller read in a week, you might stratify the population by college graduates and less educated people. If an initial quick survey told you that, in 100 residents, 60 were college graduates and 40 were not, you could decide to sample college graduates and non-graduates at a 6/4 ratio during phase two of your study.

## References

Shalabh, Sampling Theory Chapter 8. Retrieved from http://home.iitk.ac.in/~shalab/sampling/chapter8-sampling-double-sampling.pdf on January 28, 2018

Penn State STAT 506 Sampling Theory and Methods Course Materials

Retrieved from https://onlinecourses.science.psu.edu/stat506/node/48 on January 28, 2018

Encyclopedia of Statistical Sciences: Double Sampling

Retrieved from http://onlinelibrary.wiley.com/doi/10.1002/0471667196.ess0525.pub2/abstract on January 28, 2018

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