Free online educational courses may not be democratizing education as much as proponents believe, a new study reports.

John D. Hansen, a doctoral student at Harvard University’s School of Education, and his colleagues looked at registration and completion patterns in 68 massive open online courses, or MOOCs, offered by Harvard and M.I.T. The data covered 164,198 participants aged 13 to 69.

In a study published in the journal Science, Mr. Hansen and his colleagues reported that people living in more affluent neighborhoods were more likely to register and complete MOOCs. Each increase of $20,000 in neighborhood median income raised the odds of participation in a MOOC by 27 percent, the researchers found.

Yet the vast majority of MOOC participants are not the very affluent, who are comparatively small in number. Mr. Hansen said that it ought to be possible to adapt or redesign online courses so that they are more appealing and accessible to lower-income people.