Sometimes, spending money to promote a candidate, even a lot of money, doesn’t make a difference.

Until the Republican presidential contenders shifted their focus to South Carolina this week, Texas Gov. Rick Perry had the television airwaves in the state to himself for about nine weeks — while his poll numbers sank.

An independent group that is helping Perry has spent nearly $2 million on advertising in South Carolina since early November. During that period, Perry has fallen from 11 percent support in a CNN/Time magazine poll at the end of October to 5 percent in a survey taken last week.

The 2012 presidential primary season has been marked by heavy spending from super PACs, independent groups with the sole purpose of putting large campaign contributions behind many of the top candidates. The spending has prompted hand-wringing from good-government groups and pundits concerned about the role of money in politics.

But the rise and fall of so many GOP candidates this cycle has shown that it’s surprisingly easy to spend millions of dollars to little or no effect.

In New Hampshire, data on television spending show that former Utah governor Jon Huntsman Jr. and his super PAC spent twice as much per vote as former Massachusetts governor Mitt Romney and his supporters. And Romney won the state’s primary on Tuesday with more than twice as many votes as Huntsman, who finished third.

In Iowa, Perry and his super PAC spent 20 times as much per vote as supporters of the second-place finisher, former senator Rick Santorum (Pa.).

A spokesman for Make Us Great Again, the PAC backing Perry, declined to comment and the Perry campaign did not respond to requests.

“Money doesn’t buy outcomes,” said Richard L. Hasen, a law professor at the University of California at Irvine who studies campaign finance. “The money gets you another look — you can’t avoid looking at Perry when there’s advertising everywhere — but it can’t overcome an overwhelming negative impression.”

Our Destiny PAC, which is backing Huntsman, spent $2.5 million ahead of the New Hampshire primary. The former governor did get a bump in the polls after the ads began airing in November, but his third-place finish there leaves little chance that he will be a serious contender in upcoming primaries.

Even in the cases in which super-PAC spending has been blamed for major changes in the race, there is evidence to the contrary.

Former House speaker Newt Gingrich (Ga.) has denounced the negative advertising sponsored by a Romney super PAC in Iowa before the Jan. 3 caucuses there. Gingrich said he was “Romney-boated,” a reference to ads featuring the group Swift Vets and POWs for Truth that conservatives ran against Sen. John F. Kerry (Mass.), the 2004 Democratic nominee.

“For a state this size, to spend that number of dollars in negative ads aimed at one candidate is pretty amazing,” Gingrich said at a news conference in Iowa.

But undermining his argument is the fact that Gingrich’s poll numbers fell nationally as well during the same period.

Gingrich dropped 13 percentage points in a Des Moines Register poll of Iowa caucus-goers at the end of December, compared with a month earlier. He fell 14 points in a national daily tracking poll by Gallup. A spokesman for the candidate did not respond to a request for comment.

The ads — and Gingrich’s decline in the polls — coincided with heightened media attention on the former speaker’s record and criticism by other candidates, both of which could have had as much effect as the advertising in Iowa.

Also, a surge in support for Santorum in the final weeks before the Iowa contest appears to have had little to do with television advertising. Spending on Santorum ads was a quarter of the amount spent on behalf of Romney.

Santorum made up for the difference with face time and plentiful media coverage once he began to rise in the polls. And a series of contentious television debates have given candidates direct access to voters — for free.

“Nobody can create an ad that’s better than a candidate meeting someone person to person,” said John Brabender, a Santorum adviser.

The advantages of a well-funded super PAC could become more important in upcoming primaries, which take place in bigger states in which television advertising is needed to reach most voters.

Santorum’s campaign refrained from advertising in Iowa and New Hampshire, small states where voters have come to expect personal interaction. The campaign plans to spend $1.5 million on television in South Carolina before the Jan. 21 primary there, Brabender said.

The Red White and Blue Fund, the biggest PAC backing Santorum, said it will run nearly $800,000 worth of ads in the state and has plans for more.

“Certainly that will be helpful as well,” Brabender said.