The process of selecting students likely to complete science, technology, engineering and mathematics (STEM) doctoral programs has not changed greatly over the last few decades and still relies heavily on Graduate Record Examination (GRE) scores in most U.S. universities. It has been long debated whether the GRE is an appropriate selection tool and whether overreliance on GRE scores may compromise admission of students historically underrepresented in STEM. Despite many concerns about the test, there are few studies examining the efficacy of the GRE in predicting PhD completion and even fewer examining this question in STEM fields. For the present study, we took advantage of a long-lived collaboration among institutions in the Northeast Alliance for Graduate Education and the Professoriate (NEAGEP) to gather comparable data on GRE scores and PhD completion for 1805 U.S./Permanent Resident STEM doctoral students in four state flagship institutions. We found that GRE Verbal (GRE V) and GRE Quantitative (GRE Q) scores were similar for women who completed STEM PhD degrees and those who left programs. Remarkably, GRE scores were significantly higher for men who left than counterparts who completed STEM PhD degrees. In fact, men in the lower quartiles of GRE V or Q scores finished degrees more often than those in the highest quartile. This pattern held for each of the four institutions in the study and for the cohort of male engineering students across institutions. GRE scores also failed to predict time to degree or to identify students who would leave during the first year of their programs. Our results suggests that GRE scores are not an effective tool for identifying students who will be successful in completing STEM doctoral programs. Considering the high cost of attrition from PhD programs and its impact on future leadership for the U.S. STEM workforce, we suggest that it is time to develop more effective and inclusive admissions strategies.