Graduate Is this a Formal (Statistical) Fallacy?

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The discussion centers on a potential formal fallacy related to analyzing non-representative subsamples of a population, leading to erroneous conclusions about variable effects. Examples provided include the GRE's predictive power, height's correlation with scoring in basketball, and hand-eye coordination's relationship with baseball performance. Participants explore whether this issue has a specific name, suggesting concepts like sampling bias and the fallacy of composition as relevant but not entirely fitting. The conversation also touches on Berkson's Paradox as a related idea. The thread seeks clarity on the formalization of this statistical fallacy.
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Fallacy on a supposed falsification of a correlation by looking at a subset of the population.
Hi All,
I have recently read about a fallacy that seems to be based on looking at a non-representative subsample of the population. I would like to know if this goes by a name and if it has been formalized. It just seems the problem is that of considering a variable within a subpopulation and not within the whole population ( here population referring to actual people). It is then concluded that the variable in question has no effect on other variables of interest.

Here are two examples:
1) The GRE test is artificial, without any real predictive power: It does not correlate with GPA in graduate school, nor with other measures of success. But, when considered within the population of , say, adults, a high GRE test does correlate highly with variables as income, job satisfaction, etc.

2) Like in 1), we can argue that height does not highly correlate with the ability to score: even as NBA players differ in several inches in height, their total points totals are the same

3)Hand-eye coordination and batting average in Baseball. Say we could find numerical measures. These do not correlate with batting average, WAR or slugging average.

Does this fallacy have a name? Is it based on other than just considering a subsample, a sort of survivorship bias?
 
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It isn't the same thing per se, but this feels 'close' to Berkson's Paradox
 
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First trick I learned this one a long time ago and have used it to entertain and amuse young kids. Ask your friend to write down a three-digit number without showing it to you. Then ask him or her to rearrange the digits to form a new three-digit number. After that, write whichever is the larger number above the other number, and then subtract the smaller from the larger, making sure that you don't see any of the numbers. Then ask the young "victim" to tell you any two of the digits of the...

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