A FEW years ago, the sociologists Becky Pettit and Bryan Sykes tried to quantify a worrisome phenomenon: the growing proportion of black men imprisoned by age 20. Focusing on those born between 1975 and 1979 who later dropped out of high school, they noticed an anomaly. “Our initial efforts,” Dr. Pettit recalls, “implied that more young, black, low-skill men had been to prison than were alive.”

It took her no time to resolve the inconsistency: corrections officials count actual prisoners, a captive audience; sociologists and census-takers typically undercount prisoners and former inmates living on the edge of society.

The real problem, as Dr. Pettit sees it, is that imprisoned black men aren’t figured into statistics about the standing of African-Americans. The consequence, she says, is an overstatement of black progress in education, employment, wages and voting participation.

Dr. Pettit, of the University of Washington, has now presented her research in “Invisible Men: Mass Incarceration and the Myth of Black Progress,” published by the Russell Sage Foundation. Among her conclusions:

¶ Among male high school dropouts born between 1975 and 1979, 68 percent of blacks (compared with 28 percent of whites) had been imprisoned at some point by 2009, and 37 percent of blacks (compared with 12 percent of whites) were incarcerated that year.