A year and-a-half later, analysts and academics still have reached no real consensus on how Donald Trump pulled it off in the 2016 presidential election. But three Ohio State University researchers have a new — and controversial — study that shows a key portion of Trump voters were very susceptible to the influence of fake news.

Paul Beck, longtime OSU political science professor, said the post-election deep dive focused on voters who supported Barack Obama in 2012 but not Hillary Clinton in 2016. About 77 percent of Obama voters stuck with Clinton, so if she had gotten only a handful more, she would be president.

"The real key in 2016 is what happened to the Obama voters?" Beck said.

He stressed that the study did not prove a cause-and-effect directly linking false information and Trump’s victory.

"Whether it’s large enough to really make a difference, we can’t say," he said. "But it’s very conceivable that it really affected the outcome of the election."

Beck noted that Clinton lost to Trump by a combined 77,744 votes in the closely contested states of Pennsylvania, Michigan and Wisconsin — a mere 0.6 percent of the votes cast.

"Even a modest impact of fake news might have been decisive," concluded Beck and co-authors Richard Gunther and Erik C. Nisbet in what they say is the first examination of the affect of fake news on the 2016 vote.

"Indeed, given the very narrow margins of victory by Donald Trump in key battleground states, this impact may have been sufficient to deprive Hillary Clinton of a victory in the Electoral College."

Researchers asked survey respondents 281 questions about the 2016 election, including their take on three fake news statements widely disseminated on social media and even via some broadcast outlets. Two were false negative statements about Clinton and one was a false positive statement involving Trump.

The former Obama voters who agreed with one or more of the fake news items were 4.5 times as likely to have rejected Clinton as those who agreed with none of the three false items.

Put another way, among those Obama voters who didn’t believe any of the three fake news stories, 89 percent cast ballots for Clinton. For those who believed one of the fake news items, 61 percent voted for Clinton. And of those who believed two or three of the false statements, 17 percent supported Clinton at the polls.

Beck emphasized that this conclusion does not support the condescending contention by some that Trump won because of uneducated white voters. While conducting the study, differences in education were taken into account — as were a host of variables other than fake news that could have explained the Obama voters’ decision to vote Republican.

"I started out thinking that once we slapped on the controls, fake news would go away," Beck says. But after the multiple regression analysis calculated the impact of numerous possible factors, belief in the false stories wound up as the main one that distinguished the defectors from the Democratic Party.

"These data strongly suggest … that exposure to fake news did have a significant impact on voting decisions," the study concluded.

Again, that's not proof; the study itself notes: "It is possible, for example, that someone who disliked Clinton and chose not to vote for her might endorse these false statements after the fact in order to rationalize their voting decision."

The data for the research stemmed from an Internet survey conducted for the authors by YouGov, an Internet survey organization, from Dec. 5, 2016, through Jan. 6, 2017. Initial contacts were whittled to a final sample of 1,600 respondents on the basis of gender, age, race, education, ideology, and political interest — including 585 who voted for Obama in 2012 and used the internet or social media as an information source.

The three "fake news" statements used in the study:

• "Hillary Clinton is in very poor health due to a serious illness."

• "Pope Francis endorsed Donald Trump for president prior to the election."

• "During her time as U.S. secretary of state, Hillary Clinton approved weapon sales to Islamic jihadists, including ISIS."

Beck was asked if any of the three fake news items originated from Russian meddling in the presidential campaign.

"Not that we know of," he replied.