“Early in her career, Virginia M. Rometty, I.B.M.’s next chief executive, was offered a big job, but she felt she did not have enough experience. So she told the recruiter she needed time to think about it.

That night, her husband asked her, “Do you think a man would have ever answered that question that way?”

“Analysts said that perhaps the most important strategy at I.B.M., which also had early inclusion programs for minorities, disabled and gay employees, is its formal mentorship program.”