A statistics graduate of City College (now City U), New York in 1952, Shapiro took an MS in industrial engineering at Columbia U in 1954. After a period working as a statistician in the Army Chemical Corps, he joined the General Electric Corporation, obtaining his MS (1960) and PhD (1963) in statistics at Rutgers U. He was co-author of the 1965 paper that introduced the Shapiro–Wilk test and of the 1972 paper introducing the Shapiro–Francia test. In 1972 he joined the faculty at Florida International U.