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There was a small study that came out recently on biorxiv, with 29 PhD students with GREs all over the place -

>GRE scores, while collected at admission, were not used or consulted for admissions decisions and comprise the full range of percentiles from 1% to 91%. We report on the 29 students recruited to the Vanderbilt IMSD from 2007-2011 who have completed the program as of summer 2017. While the data set is not large, the predictive trends between GRE and long-term graduate outcomes (publications, first author publications, time to degree, predoctoral fellowship awards, and faculty evaluations) are remarkably null and there is sufficient precision to rule out even mild relationships between GRE and these outcomes. Career outcomes are encouraging; many students are in postdocs, and the rest are in stage-appropriate career environments for such a cohort, including tenure track faculty, biotech and entrepreneurship careers.

Now a GRE isn't a GPA (one's a specific test, one is your grades' average), but both are being used for university admissions, and I reckon both are not good predictors.

Edit: Link: https://www.biorxiv.org/content/early/2018/07/20/373225



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