The study found that popular reactions to major policy news on Twitter oftentimes conflicts or even is the opposite of the most popular view found in surveys. As an example the Pew survey notes that in February, when a federal court, found a California ban on same-sex marriage unconstitutional the reaction on Twitter was "quite positive." But in polling, 33 percent supported the ruling while 44 percent said they were "disappointed or angry" about the federal court's decision.

During the last presidential election, a Twitter analysis found 77 percent of comments about President Obama's reelection on Twitter were positive and 23 percent were negative. But a national survey of voters showed that 52 percent were pleased with Obama's reelection while 45 percent were not pleased.

The tone of tweets varies also, the Pew study found. Negativity on Twitter to both Obama and Mitt Romney outnumbered positive comments on Twitter throughout most of the 2012 presidential campaign. But from September through November, negativity reactions on Twitter were directed more toward Romney than Obama.

That's not to say that sentiment toward Obama is always more positive on Twitter. The Pew study found that, in a national survey shortly after the 2012 State of the Union address, 42 percent had a positive reaction to the president's speech while 27 percent had a negative opinion of the speech. By contrast, an analysis of Twitter found that 40 percent had a negative opinion of Obama's speech while 21 percent had a positive reaction.

The Pew study cautions that the sentiment on Twitter is not representative of the public's view.

"Twitter users are not representative of the public. Most notably, Twitter users are considerably younger than the general public and more likely to be Democrats or lean toward the Democratic Party," the study says.

The study also notes that people who use Twitter don't weigh in on every major policy topic of the day. The study found that that Twitter users who tweeted about the California same-sex marriage ban ruling were unlikely to tweet about Obama's second inauguration or who Romney chose as his running mate.

"Overall, the reaction to political events on Twitter reflects a combination of the unique profile of active Twitter users and the extent to which events engage different communities and draw the comments of active users," the study's findings say. "While this provides an interesting look into how communities of interest respond to different circumstances, it does not reliably correlate with the overall reaction of adults nationwide."

The data Pew used for the analysis of Twitter comes from a combination of all public tweets.