How can the news media attract an audience that’s skeptical of journalism’s most deeply ingrained principles? Well, consider two different treatments of the same story.

In our first example, the headline reads, “New Recreation Center For Low-Income Neighborhood A Casualty Of Parks Scandal.” The lead: “A project aimed at helping the city’s most marginalized, low-income neighborhood has been abandoned in the wake of a misuse of city funds by the parks director, according to documents obtained by a local media investigation.”

That seems straightforward enough — newsy and with an emphasis on the victims of a corrupt city official.

Now, here’s the second version. The headline: “Parks Boss Deceived Mayor, Misused Taxpayer Money.” The lead: “The city’s parks director intentionally defied the orders of the mayor and diverted city money from a key recreation project to businesses owned by his friends and family, according to documents obtained by a local media investigation.”

This treatment introduces the mayor as a key player right at the top and portrays her or him as an authority figure who was betrayed by an underling. And that, in turn, makes a significant difference in how the story is perceived, according to a major new study by the Media Insight Project, a collaboration of the American Press Institute and the Associated Press-NORC Center for Public Affairs Research.

As the study’s authors explain it, the first version appeals mainly to readers who place a high value on caring and fairness, which correlates with stronger support for journalism. The second appeals to readers who value loyalty and authority, which correlates with lower support for journalism. The good news is that the second version broadened the potential audience for the story without diminishing its appeal among those who value caring and fairness.

At this point you might ask why I’m hacking my way through the weeds of the study rather than focusing on the topline results. The reason is that the major takeaways just seem too depressing unless you take a close look at how they might be applied in the service of making journalism better and more appealing.

The survey of more than 2,700 Americans found majority support — 67% — for only one of the five core journalism values identified by the authors, “the idea that more facts get us closer to the truth.” By contrast, just 29% embraced a focus on social problems. Giving a voice to the less powerful, transparency and oversight — that is, the watchdog function of journalism that is so often stressed as being of crucial importance to democratic governance — all fall somewhere between 44% and 50%. Only 11% of respondents support all five functions.

As the report puts it, “When journalists say they are just doing their jobs, in other words, the problem is many people harbor doubts about what the job should be.”

The study also attempts to match those five core functions with some pretty sophisticated personality modeling based on the work of the social psychologist Jonathan Haidt and his colleagues. They identified five moral foundations that govern us: care versus harm, fairness versus cheating, loyalty versus betrayal, authority versus subversion and purity versus degradation.

The first two tend to be associated with liberals and Democrats, who are more trusting of journalism. The next three are more associated with conservatives and Republicans, who are less trusting. But as the two versions of the same scandal story demonstrate, tweaks can sometimes be made that don’t alter the substance of the story and that can broaden its appeal so that both liberals and conservatives will read it.

Dispiriting though the topline findings may be, they contain actionable information — which puts this at a considerably higher plane than your typical survey showing that, yes, the public still hates the press.

“I must confess that my first impulse was to resist these findings,” wrote Washington Post media columnist Margaret Sullivan. “After all, I’ve spent decades with the ideas described above as my lodestar, convinced that journalism serves the public good. And after all, investigative journalism is built on the idea of being society’s watchdog.

“However, given that trust in the news media has fallen from about 70% in the early 1970s to about 40% now, according to Gallup — it seems worth viewing this report with an open mind.”

As Tom Rosenstiel, the executive director of the American Press Institute, told Sullivan, “This at least opens a new window. It gets us out of the endless loop.”

For years, and especially since Election Day 2016, the mainstream media have been wringing their collective hands and wondering how they can understand conservatives, Republicans and Trump voters, three categories that overlap mostly but not entirely. The New York Times, in particular, has subjected us to endless stories from the heartland that could all be headlined, “Trump Supporters Support Trump.”

The Media Insight Project may show us that there’s a different, more nuanced way of understanding the public — and that, by appealing to their sense of values, journalism may be able to bridge gaps that often seem unbridgeable.

GBH News contributor Dan Kennedy’s blog, Media Nation, is online at dankennedy.net.