Liberal writers are zeroing in on a new study from Pew’s Project for Excellence in Journalism that found Barack Obama has been subjected to far more “negative” coverage than any of the Republican presidential candidates. The graphic accompanying the study is dramatic:

Slam dunk, right?

One of Eric Boehlert’s blog items at Media Matters is headlined “So Much for the Liberal Media.” In another post he acknowledges that there have been criticisms of the Pew methodology in the past, but the real issue here is how right-wing critics will react to the numbers.

Steve Benen at Washington Monthly makes a similar point:

It’s simply taken as a given in Republican circles that President Obama enjoys favorable coverage from major media outlets. This is generally pretty hard to believe among non-conservatives, but it’s helpful to take this out of the realm of perception and into more quantifiable analysis.

If the point that liberals are making is that the liberal media conspiracy that exists in the minds of conservatives bears no resemblance to reality, they’re right. But we didn’t need a new study to confirm this.

A more important question (for media critics at least) is whether the study’s methodology is sound. And this is where things get a little muddy.

Part of the Pew study is attempting to measure “tone.” This involves making some decisions about how you would measure that, as the study makes clear: “The unit of measure of tone is each assertion or statement contained in a story or blog post.” Pew set up a computer algorithm to capture news content and code it accordingly.

The report gives an example of a Gannett story about Herman Cain’s poll numbers. The report stated that he was making “good impressions,” according to the poll’s findings. Thus this would be coded as a “positive” assertion. A story that quoted someone speaking about Michele Bachmann’s migraines is a “negative” assertion. The report explained, “A story that is entirely about a poll showing Mitt Romney ahead of the Republican field—and that his lead is growing, would be a good example to put in the ‘positive’ category.”

It doesn’t take long to spot the problem here. Candidates performing well are far more likely to rack up “positive” coverage, even if that coverage is, strictly speaking, unremarkable campaign reporting about fundraising, polls and so on. Newt Gingrich’s campaign scores a lot of “negative” coverage. But given the state of his campaign, that is completely unsurprising—and does not reveal a media “bias” against Gingrich.

This would seem to be the main explanation for “negative” coverage of Obama. A number of Republican politicians are running to challenge him, and are thus likely to criticize his record. Those comments would be recorded as “negative” coverage. But so would coverage that simply relates bad news—Pew explains:

Even the week of May 2–8, immediately after the raid that killed Osama bin Laden, Obama’s coverage was overwhelmingly negative. One reason is that many of the references to his role in the hunt for bin Laden were matched by skepticism that he would receive any long-term political benefit from it. Another was that the bin Laden news was tempered with news about the nation’s economy.

“A nation surly over rising gas prices, stubbornly high unemployment and nasty partisan politics poured into the streets to wildly cheer President Barack Obama’s announcement that Osama bin Laden, the world’s most wanted man, had been killed by U.S. forces after a decade-long manhunt,” stated a May 2 AP story. “The outcome could not have come at a better time for Obama, sagging in the polls as he embarks on his re-election campaign.”

They don’t make it perfectly clear, but one can assume that a story like this would be coded as “negative”—because it mentions things like unemployment and partisanship.

The problem is that a study like this seems to confuse media bias with bad news. It’s doubtful that Pew’s point was to suggest that there is an overwhelming anti-Obama bias in the national media. But that’s one conclusion people are likely to draw when a study talks about “positive” and “negative” media coverage.

It’s hard to suggest with a straight face that politicians deserve coverage that is half friendly, half critical at all times. But without some non-arbitrary way to determine the tone of coverage a politician should be getting—and what would that look like, exactly?—it’s hard to turn a count of “positive” and “negative” coverage into a gauge of media bias.