PROVIDENCE — Pollsters are like weather forecasters. People love to hate them when they’re wrong.

“When I meet someone now I tell them I’m a used-car salesman rather than a pollster,” jokes Darrell West, Brown University political science professor and longtime pollster. “I seem to get a better response.”

The science of measuring public opinion has taken its lumps this election cycle, especially in the Democratic primary race between Senators Hillary Clinton and Barack Obama. Starting with the first primary in New Hampshire last month, some of the nation’s most respected public survey firms have struggled to accurately gauge public opinion.

Pollsters say this race is a perfect storm of uncertainty, with a volatile electorate, well-financed campaigns, and record voter turnout that makes predicting who will show up to vote more difficult.

In New Hampshire, the major polls put Obama ahead by an average of about 8 points in the days before the vote, according to the poll-tracking Web site RealClearPolitics.com. Clinton narrowly won the state, and the political junkies who devour polls were left to wonder what happened.

Many more recent polls have vastly underestimated the margins of Obama’s big victories in his streak of 11 consecutive primary and caucus wins.

“Polling a primary is far more difficult than polling a general election,” says national pollster Scott Rasmussen. “You’ve never seen anything like this on the Democratic side.”

Democrats this year are generally pleased with both of their candidates. “They’re having a hard time deciding, and they’re deciding late,” he said. “One of the things we’ve been pointing out on our polls recently is that many of these voters are saying they still might change their mind before voting. It’s typically 25 or 30 percent. That just automatically makes it fluid and very difficult to poll.”

Rasmussen expects the general election, between either Clinton or Obama and Republican John McCain, to be much easier for pollsters because of the wider policy differences between the candidates — he expects fewer voters will be changing their minds.

Three polls this month suggest Clinton is leading in Rhode Island.

West polled 474 likely voters Feb. 9-10 and calculated that Clinton leads, 36 percent to 28 percent.

In a survey of 1,035 likely voters last Saturday, Rasmussen has Clinton ahead, 53-38.

Another polling firm, American Research Group, polled 600 voters Feb. 20-21. ARG has Clinton ahead, 52-40.

Channel 12 expects to release the results of a Democratic primary poll tomorrow. Pollster Joseph Fleming refused to disclose the results, except to say that “this race looks fluid,” meaning that changes in voter allegiance may have taken place over the last few weeks.

To the casual observer of politics, polling may seem like magic or luck. In reality, it combines both science and art.

Using mathematics and the laws of probability, a trained pollster takes a random sample of voters to gather opinions on an election. From that sample, the laws of probability allow the pollster to calculate the results that will stand for the whole.

But the pollster has to calculate the degree the sample differs from the whole population. This is known as the margin of error; no poll can be perfect. Based on the law of probability, in such a sample of say 1,200 respondents, 19 of 20 polls, — or 95 percent — will be accurate to within an error margin of about 3 percentage points.

Despite a high degree of science and mathematics, pollsters always caution that a survey is not a predictor; it measures only a glimpse of an election at a specific point in time.

A good poll will rotate the questions so the order in which questions are asked will not influence the results. “The way questions are asked is crucial,” says Tad Devine, the Rhode Island native who has served as a strategist for several Democratic presidential campaigns. “If you ask someone ‘Are you for Obama, are you for Clinton or are you undecided,’ [that] will give you a different result than asking undecided voters which candidate they are leaning toward.”

Polling has come a long way since the days when newspapers conducted informal straw polls and printed the results as gospel. In 1936, Literary Digest magazine made its infamous prediction that Republican Alf Landon would defeat incumbent Democrat Franklin D. Roosevelt. The magazine sent ballots to millions of voters, but it included only those who subscribed to magazines or had home telephones — thus eliminating people who couldn’t afford either and tended to vote Democratic.

After that election, George Gallup refined the science of polling by advancing the theory that a poll could be accurate within a margin of error if voters from all regions of the country and levels of wealth had an equal chance to be interviewed.

Nowadays, most polls work by using a random sample of telephone numbers that are dialed repeatedly to try to reach every name on the list. The results are weighted to ensure that no segment of the voting population, such as women or minorities, are overrepresented.

Devine, the Democratic strategist, says local pollsters who have a history in a particular city or state probably do a better job of figuring out local quirks. For example, Devine said, the Iowa caucus polls are all over the map, except for the one run by the Des Moines Register, the most influential of Iowa newspapers and a media outlet that has been polling the local caucuses since the 1970s.

Among the technical roadblocks that face pollsters nowadays are caller ID and telephone answering machines. A generation ago, 70 or 80 percent of people called randomly answered pollsters’ questions. That number has dropped to less than 35 percent, and in some cases as low as 15 or 20 percent. Fleming, the Channel 12 pollster, said he had to make 4,000 calls in Rhode Island to get an accurate sample of 400 for the poll being released tomorrow.

Cell phones are another problem for pollsters. Some voters just don’t have landlines, and pollsters are not reaching them.

“It is a huge phenomenon among younger adults under 25,” Rasmussen said. “It is a growing concern. By election 2012 we’ll have to totally rethink the way we do things to address cell phone-only people.” The estimate for this year is that 6 percent of the electorate will be wireless-only, he said. “And there is a lot of evidence that they are not that much different from their peer group as far as their political views. So what we’re doing is adjusting the number of young people in the sample to recognize the fact that we’re not getting them all.

“It’s not as if nothing has changed in telephone polling in 50 years and all of a sudden cell phones have changed the game,” Rasmussen said. “The cell phone phenomenon is very significant. But it’s something people will work around and the reason is very simple: people want the information.”

As an experiment, Rasmussen has launched a “prediction market” on his Web site, which encourages people to trade futures on which candidate they think will win, like playing a political stock market. Rasmussen’s prediction market has been very accurate in all the primary states so far, he says, with the exception of New Hampshire.

smackay@projo.com