A new survey finds that while most of the public knows society has a long way to go before women will be fully equal, people are poorly informed about feminism and key women’s issues.

The poll, conducted by PerryUndem Research/Communication for the Ms. Foundation for Women, surveyed a representative sampling of adults nationwide. The poll over-sampled people of color in order to get better data on certain demographic groups.

The survey has both good and bad news for feminists. It found that while respondents believe in equality for women, many have a negative view of the word “feminism,” are divided on whether women of color face more barriers to equality than white women, and have a narrow idea of what “women’s issues” means.

Sixteen percent of respondents identified as “feminist” when asked. However, challenging people’s preconceptions about the word made a huge difference. Those self-identifying as “feminist” jumped to 52 percent once they were given a definition of feminism as “a belief in political, economic, and social equality across genders.”

The top responses for why people didn’t identify as a feminist were “Feminists are too radical/extreme” (15 percent) and “Everyone should be equal regardless of gender” (13 percent). Others who responded said they didn’t like the label, are a man, or think men and women have different roles or strengths, among other responses.

The study also found that U.S. residents have a narrow idea of what “women’s issues” means. 

Answering an open-ended question about what they think a 2016 presidential candidate means by “women’s issues,” most said it meant equal pay or abortion rights.

Fourteen percent said “equal opportunities in the work force,” and a smaller minority of respondents thought of child care, parenting, birth control, healthcare, sexual assault, or domestic violence.

On another question that could have 2016 electoral implications, large majorities across party, race, and gender lines thought that men and women have different views (63 percent) and different strengths (73 percent) when it comes to solving problems.

“I wouldn’t have expected that big a difference,” PerryUndem partner Tresa Undem told reporters Tuesday.

Good news in the study for feminists is that huge majorities believe the feminist project isn’t over, even if they may feel ambivalent about the word “feminism.”

Seventy-nine percent of respondents said there is “still more work to be done” in order to achieve “full equality for women in work, life, and politics.” Eighty-two percent said they believe in “equality across genders,” and 77 percent think that women should have equal positions of power in solving community and national problems.

But many of those people seem confused about how much power women have. When asked who is in more positions of power to fix problems, men or women, the respondents were mostly split between “men” and “both equally.”  

More people thought women and men had equal power at the community level (44 percent) than at the national level (33 percent). But that still means that a third of respondents don’t seem to realize that women make up just 20 percent of Congress and the United States has never had a female president.

Respondents were also divided about whether women of color face more barriers to equality than white women—a question that doesn’t seem to have been asked in other surveys, Undem said.

Slightly more than half of respondents said that women of color have “equal opportunities” to white women, and slightly less than half said that they don’t have equal opportunities to white women. 

Undem said that African-American men and women saw more barriers to equality for women of color than other groups did. She was also surprised to learn, she said, that neither white nor Hispanic women noticed more inequality on this question than men in their same groups.

A vast body of research shows that women of color make less money, face more discrimination, and have worse access to health care than white women, along with other disparities.

In their own communities, respondents were most worried about economic issues like an inadequate number of good-paying jobs or not being able to make ends meet, although they didn’t always connect these issues to gender.

A majority (64 percent) thought that women and men have equal trouble finding good-paying jobs, for instance. Among those who did notice a disparity, however, respondents were more than three times more likely to say women had trouble finding good-paying jobs (26 percent) than men (8 percent).