The harassment of women online has emerged as a major subject of concern recently—even, perhaps, “tomorrow’s civil rights agenda,” according to feminist commentator Amanda Hess who brought this issue into the spotlight with a long article in Pacific Standard magazine last January. Highly publicized events such as the mass release of stolen nude celebrity photos—nearly all of women—and threats against several female critics of sexism in videogames have bolstered claims that the Internet is a cesspool of misogyny, with women routinely subjected to vile abuse and threats for having an opinion or simply for being female. But are these claims true? A new study from the Pew Research Center shows that, while the Internet can indeed be a nasty place, it is not uniquely so for women. This finding is consistent with earlier research. Yet it has been reported in ways that often lean toward the familiar narrative of women in jeopardy—a narrative that is distorted and ultimately damaging to women.

The Pew online harassment study, based on a survey of nearly 3,000 Internet users last June, found that 44 percent of men and 37 percent of women had experienced some form of online abuse, from name-calling to physical threats and stalking. The biggest gender gap was in the fairly mild category of being called offensive names, experienced by nearly a third of men on the Internet but only 22 percent of female users. However, more men—10 percent, compared to 6 percent of women—also reported being physically threatened. Women were more likely than men to say they had been sexually harassed (9 percent versus 6 percent) and stalked (10 percent versus 7 percent); sustained harassment was reported by 8 percent of men and 7 percent of women. Interestingly, the survey also found that people perceived most online spaces to be female-friendly; 18 percent even said that the social media were more “welcoming” to women than to men, while only five percent agreed with the reverse.

Meanwhile many articles on the study emphasized the perils for women. Sample headlines: “Pew: Women Suffering Online Harassment Worse Than Men.” “For Women, the Internet Can Be a Scary Place.” “Everyone’s a Jerk to Everyone Online, But Young Women Have It the Worst.” Some commentators even expressed frustration and disbelief that so few Netizens saw online life as a hostile environment for women.

The women-as-victims angle focused mainly on the survey’s youngest respondents, ages 18 to 24. Twenty-six percent of women in this demographic said they had experienced online stalking, compared to 7 percent of men. (“Sustained harassment” was reported at roughly equal rates of 18 and 16 percent.) A quarter of the young women and 13 percent of the young men said they had been sexually harassed on the Internet.

However, an important caveat was overlooked: these figures are far less reliable than the study’s general results. While the survey had an overall margin of error of 2.4 percentage points, it was almost 11 percent for the under-25 sample of just 137 women and 126 men. Given that slightly older women, 25 to 29, were far less likely to report online stalking or sexual harassment, dramatic conclusions seem premature.

Women of all ages were more frequently upset by Internet harassment: 38 percent of women who had experienced it described the most recent such incident as “extremely” or “very” upsetting, while 17 percent of the men did. But these responses could be interpreted in a number of ways. Do women suffer worse abuse? Do they find online harassment more distressing because it’s more likely to come from friends or family, and thus to be linked to personal problems? Do they feel more vulnerable, or are they more willing to admit to being upset by words on a screen? Is it a combination of many factors? Even the data on specific forms of abuse lend themselves to subjective judgment, since the survey did not define such terms as “sexual harassment” or “stalking.”

It also worth noting that a Pew Internet use survey last year found men and women to be at virtually equal risk for the most severe consequences of online conflict. Five percent of women felt that something that happened online had put them in physical danger—a figure cited in Hess’s Pacific Standard article as evidence that the Web was a hostile environment for women. Yet the figure for men was three percent, a gap within the poll’s margin of error.

A survey released in February 2013 by the McAffee security technology company challenges another common belief about gender and danger online: that “revenge porn” victims are overwhelmingly women. Eight percent of American women 18 to 54 said they had been threatened with having a sexually embarrassing photo exposed online—but 12 percent of men also reported such an experience. What’s more, nearly two-thirds of the threats against men but only half of the ones against women were carried out.

Then why has the notion that women are singled out for rampant online abuse become entrenched media wisdom? Perhaps because abuse targeting men is far less likely to be noticed and acknowledged.

Thus, in a post arguing that the virulent backlash against feminist media analyst Anita Sarkeesian’s critiques of sexism in videogames is driven by misogynistic rage, progressive blogger Ally Fogg asks why gamers are picking on Sarkeesian and not “evangelical Christians like Jack Thompson,” a crusader against violent games. But this “gotcha” question is comically wrong. When Thompson was in the spotlight seven or eight years ago, diatribes against him on gaming websites and forums included references to emasculation and rape. While an interactive game inviting players to beat up a likeness of Sarkeesian two years ago was deplored and quickly removed, there was no such outrage over four games in 2006 making Thompson a target of virtual violence and even murder. The game blog Kotaku, which now takes a strong stand against the harassment of women in gaming culture, fought a successful legal battle against Thompson’s demand to remove threats against him from its comments threads.

Such double standards are common. When Jennifer Lawrence and other female celebrities were victims of a nude photo leak, it was seen as an indictment of cultural misogyny; yet no one seemed too upset when NBA player Trey Burke and former Disney star Dylan Sprouse apologized after having their nude selfies posted online by vindictive ex-girlfriends. Threats and harassment targeting conservative male bloggers have gotten little attention while similar actions toward feminist bloggers, chronicled by Hess and others, have been treated as a war on women.

Is Internet abuse toward women more likely to be gender-based? To some extent, that too depends on definitions. A taunt toward a woman that refers to anatomy or sexuality is presumed to be sexist, while a taunt toward a man that refers to undersized genitalia or virginity is treated as a mere personal slur. An evidence-free social media charge of being a sexual predator is unlikely to be seen as a “gendered” attack, even though such charges are almost certainly directed overwhelmingly at men and can be quite devastating.

Partly, the double standard is rooted in the perception of women as a disadvantaged class. But also at work is a much more traditional, almost Victorian paternalism that sees women’s sensitivities as more fragile and worthy of protection.

While the Internet has brought us many wonderful things, it has also facilitated new forms of bullying, including some that are not only obnoxious but truly damaging, from cyberstalking to slander. It is imperative to find ways to create more recourse for victims of such abuse without infringing on protected speech. But such an effort should rely on facts rather than hype. The women-in-jeopardy narrative not only encourages women to be more fearful but promotes gender polarization, which is the way to a more hostile climate for everyone.

Contact us at letters@time.com.