While Donald Trump typically displays little tolerance for the intricacies of polling, he has in recent months taken to citing a textbook case in political science: the “Bradley effect,” named after then-Los Angeles mayor Tom Bradley, who led in the polls for California governor in 1982 but lost on election day, presumably because voters were embarrassed to tell pollsters they weren’t supporting the African-American politician. “He was supposed to win by 10 points, and he lost by 5 or something. So it’s a certain effect,” Trump said earlier this year. “Now, I have—unfortunately, maybe fortunately—the opposite effect. When I poll, I do fine. But when I run, I do much better.” Trump has also taken to calling himself “Mr. Brexit,” referring to the unexpected decision by U.K. voters to leave the European Union, despite polls suggesting that Britain would vote to stay.

The question of whether Donald Trump is, in fact, underperforming in polls because voters are embarrassed to admit they support him—the so-called reverse Bradley effect—has been a constant throughout the 2016 election. Republican strategists have long theorized the existence of millions of “secret” Trump supports, or what Trump himself has repeatedly referred to as his “silent majority.” But with less than a week to go until the election, a new POLITICO/Morning Consult study suggests that the myth of the shy Trump voter may be only half-right.

There was some evidence of a Bradley effect in Morning Consult’s survey, which was conducted last weekend and released Thursday. When speaking to a live pollster, Hillary Clinton led Trump by five points, 52 to 47, whereas if asked in an online poll or an automated call—two situations in which there was no possibility of social judgment—that gap narrowed to three points, with Clinton leading 51 to 48. Still, the effect was marginal, and Clinton won in both scenarios.

A more significant Bradley effect was visible among certain demographic groups, however. Morning Consult found that voters with a college degree supported Clinton by a 21-point margin in phone interviews, but only by a 7-point margin online. With voters making more than $50,000 a year, Clinton went from leading by 10 points to losing by one point, 50-49.

The results aren’t a slam dunk for either camp, giving the Clinton campaign a reason to breathe a small sigh of relief and Trump supporters another reason to ignore polls that show their candidate headed for a loss. But they don’t appear to suggest that there are enough bashful Trump voters to tilt the election in his favor, with just a few days remaining in the presidential race. And even if a surge of new or ambivalent voters do flood the polls on Election Day, it’s hardly a foregone conclusion that they’ll lean toward Trump. According to the Upshot’s Nate Cohn, these so-called “missing voters” may even lean toward Clinton. Whereas independent voters previously flooded the Republican primary process to vote for Trump, in the general election, the Upshot’s analysis finds this wave of unaffiliated voters supporting Clinton by 42 to 21 percent. Even newly-registered white voters—Trump’s key demographic—were less enthusiastically pro-Trump than the overall pool of white voters, breaking his way by just six points.