President Trump and his advisers and allies have spent several days aggressively denying that his incendiary rhetoric has contributed to an atmosphere of hostility after last week’s spate of politically motivated violence. Trump, for his part, blamed the “fraudulent” media, which he called “the true Enemy of the People,” for the “great anger” in the country.

But political scientists who study the interplay between political speech and public attitudes have found that elected officials play a huge role in setting the tone and parameters of a nation’s political discussions. “Elites can influence what people think and how they think about it when it comes to politics,” as Tufts University political scientist Brian F. Schaffner puts it in a working paper released earlier this year.

And in the case of Trump, in particular, Schaffner has compiled experimental evidence showing that Trump’s “offensive and prejudicial rhetoric” against some minority groups has made white Americans more likely to hold prejudicial views themselves. When Trump lashes out against a minority group, in other words, the public is listening. And many, according to Schaffner’s research, appear to be subsequently adopting his views as their own.

Norms of political speech and behavior are tricky things. In a two-party system such as ours, for instance, opposing parties are constantly working to establish firm boundaries between “acceptable” and “unacceptable” beliefs and behaviors, in part in an effort to paint the opposing side’s priorities as outside the mainstream.

In an environment of uncertainty like this one, cues from leaders are particularly important. People use statements from political leaders and prominent figures in the media to help anchor their own beliefs and preferences in the continuum of acceptability. But what happens when a politician starts making statements that fall well outside of the norms of discourse of either political party?

In Schaffner’s telling, that’s what happened when Trump came onto the scene in 2015, kicking off his campaign with a speech characterizing undocumented Mexicans in the United States as “rapists” who bring drugs and crime with them. It’s clear, given all that’s followed since then, that many Americans don’t believe remarks like these are disqualifying for higher office. But Schaffner still wondered: What effect was Trump’s dehumanizing rhetoric having on the people listening to it?

To find out, he ran a pair of survey experiments via the 2016 and 2017 Cooperative Congressional Election studies, nationally representative surveys conducted around elections. The 2016 experiment focused on a group of over 1,100 white respondents. The respondents were exposed to one or more prejudicial statements by Trump, including the remarks about Mexicans and a different comment characterizing African Americans as “thugs.” The remarks were presented in the context of a question asking respondents if they knew which candidate had made the comments.

Later in the survey, the respondents were asked an open-ended question: "In a few words, please let us know what comes to mind when you think of the following groups?” The groups in question included “Blacks, Mexicans, Whites, Politicians, the Middle Class, and Millennials.”

A control group of white respondents was exposed to nonprejudicial political statements used by the candidates — "Obama has no solutions. Obama has failed the country and its great citizens,” for example. Standard political attack material. The chief question: Were the people exposed to Trump’s prejudicial rhetoric more likely to say negative things about minorities and other groups than people who were shown nonprejudicial remarks?

In short, the answer was “yes.” Schaffner found that white respondents who were shown Trump’s remark about Mexicans were significantly more likely to characterize Mexicans using negative or offensive language in the following survey section. They were more likely to characterize millennials and black Americans offensively, too. “This suggests that norm-breaking rhetoric from elites might have consequences beyond how citizens talk about the particular group that was targeted by the elite,” Schaffner writes.

Interestingly, however, Trump’s remark about African American “thugs” did not generate a statistically significant negative effect on whites' views of other groups. The effect of Trump’s comments about Mexicans, on the other hand, was quite large. In the control group, for instance, just 16 percent of respondents characterized Mexicans in an offensive manner in the open-ended question. But 21 percent of whites shown Trump’s comments subsequently wrote offensive things about Mexicans, an increase in the likelihood of offensiveness by roughly one-third.

The second experiment, conducted in 2017, yielded roughly similar results using a different Trump comment as a primer, this one on Muslims: “If you have people coming out of mosques with hatred and death in their eyes and on their minds, we’re going to have to do something.” White respondents who viewed that remark were more likely to write negative and offensive things about Muslims.

Schaffner writes that his paper provides empirical support for the so-called “Trump effect”: “the notion that Trump’s offensive and prejudicial rhetoric on the campaign trail might cause individuals to express more prejudice toward out-groups,” as he puts it.

Schaffner’s research demonstrates that a single derogatory remark from a political leader has the ability to produce a measurable increase in prejudice among people exposed to it. What happens, then, in an environment where rhetoric once universally considered beyond the pale becomes routine?