A leading privacy group filed a formal complaint Thursday with the Federal Trade Commission over a 2012 study in which Facebook manipulated the news feeds of nearly 700,000 users of the social network to see what effect the changes would have on their emotions.

The group, the Electronic Privacy Information Center, said Facebook had deceived its users and violated the terms of a 2012 consent decree with the FTC, which is the principal regulatory agency overseeing consumer privacy in the United States.

"The company purposefully messed with people’s minds," the advocacy group wrote in its complaint. "At the time of the experiment, Facebook did not state in the Data Use Policy that user data would be used for research purposes. Facebook also failed to inform users that their personal information would be shared with researchers."

In the study, which lasted for one week in January 2012, Facebook changed the number of positive and negative posts that users saw in their feeds to see how that affected the emotional tone of the posts they made afterward. The research, which was published in an academic journal last week, found that people who were exposed to more negative material went on to write slightly more negative posts, and vice versa.

Facebook never sought formal permission from users for the study, arguing that its data use policy gave it sufficient permission to conduct the research. But the privacy group noted that at the time of the emotion study, the company’s data policy did not tell users that their personal information could be used for research purposes.

Regulators in Ireland and Britain are also asking questions about Facebook’s actions in the study.

The company has apologized and said it has since adopted stricter internal standards for reviewing studies before they are begun.

"When someone signs up for Facebook, we’ve always asked permission to use their information to provide and enhance the services we offer," Jodi Seth, a Facebook spokeswoman, said Thursday. "To suggest we conducted any corporate research without permission is complete fiction. Companies that want to improve their services use the information their customers provide, whether their privacy policy uses the word ‘research’ or not."

On Wednesday, Facebook’s chief operating officer, Sheryl Sandberg, said the company was in communication with regulators all over the world and that "this will be OK."

The FTC, as is its practice, declined to comment on the complaint.

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