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What is the restriction of range formula if you don't know the standard deviation of the unrestricted group is?

For instance, you run a selection process, 1st stage is a cognitive ability test and as a result you would not know the standard deviation of the population.

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    $\begingroup$ I'm voting to close this question as off-topic because it has a better fit within stats.stackexchange.com $\endgroup$
    – Chris Rogers
    Commented Apr 3, 2018 at 16:47
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    $\begingroup$ @chris this is very common scenario in I/O psychology, so it may be that psychology is at least as good a fit as stats stackexchange, as much as the question looks like more of a stats question at first. $\endgroup$
    – Jeromy Anglim
    Commented May 22, 2018 at 0:29

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My Answer

In this scenario, the unrestricted group is the population of individuals who are in the selection process. For example, Held and Foley (1994, Table 3) https://conservancy.umn.edu/bitstream/handle/11299/116989/v18n4p355.pdf shows the consequences of different selection ratios on validity coefficient estimations.

To summarize, the unrestricted group is the entire pool of applicants who take your test. The restricted group is the ones who are selected based on your selection criteria.

Alternative

Any cognitive ability test should have a manual, and that manual should contain validity information, including SD of the population. Many of them are normed in such a way as to make it simple (e.g., the SD of WAIS is 15, the SD of Stanford-Binet is 10). Obtain and use the values in the test manual.

However, I don't think this should be done in practice. The population of concern here isn't all working-age adults in the world/region, the population is all working-age adults in the world/region who have applied to work at the organization.

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