Groves served as a sociology professor of at the U-M and a senior research scientist at ISR. He founded the Joint Program in Survey Methodology at SRC, the first graduate program in the nation to offer master and PhD degrees in survey methodology.

Following his time at Michigan, Groves served as director of the U.S. Census Bureau (presidential appointment with Senate confirmation). He is a member of the National Academy of Sciences and of the National Academy of Medicine, and the American Academy of Arts and Sciences.