Opinion polls are expected to provide a simple answer to an important question: What are the people thinking? But the details often reveal a much more complicated picture.

Take two recent surveys — one of American Jews and one of Israelis — dealing with attitudes about President Barack Obama. The former found that support for Obama has plummeted, but a closer look revealed that the findings are virtually useless as a measure of American Jewish opinion.

The survey of Israelis, meanwhile, is scientifically solid, but the numbers provide a more complex, divided view than previously thought.

The national Quinnipiac poll released Dec. 9 found that Obama’s approval rating in the Jewish community stands at 52 percent. While the general findings were based on interviews with more than 2,000 Americans, the Jewish number was derived from a sample of just 71 respondents, for a margin of error of plus or minus 11.6 percent — a sample size that pollsters generally say makes such surveys unreliable.

The problem with such a small sample size is underscored by the up-and-down results of three Quinnipiac polls earlier this year based on responses from a similar number of U.S. Jews.

A July 27-Aug. 3 Quinnipiac survey found Obama with a 66 percent approval rating among Jews, with 30 percent disapproval.

But two months later, a Sept. 29-Oct. 5 poll — that few in the Jewish community even noticed at the time — showed Obama’s approval among Jews dropped to 46 percent, with 47 percent disapproval.

Six weeks later, however, in yet another Quinnipiac poll, Obama’s approval rating jumped to 75 percent, while his disapproval figures plummeted to 22 percent.

Finally, the latest poll, taken Dec. 1-6, showed a 52-35 split.

Given that no series of developments would seem to account for such wild swings in Jewish public opinion, the polls reinforce questions about the reliability of any survey based on such a small sample size.

The Republican Jewish Coalition, though, heralded the poll as a sign of Jews’ “buyers’ remorse” over Obama. Its executive director, Matt Brooks, said the hard numbers of the specific Quinnipiac poll were less important than what he said was an overall trend of falling support for Obama in the Jewish community.

A Gallup poll of Jews in September showed that Obama’s approval rating was 64 percent, down from 82 percent in January — a rate of decline similar to his overall drop among all Americans.

The National Jewish Democratic Council emphasized the small sample size and called the RJC’s claims “desperate and overreaching.”

Meanwhile, the New America Foundation released a poll of 1,000 Israelis last week showing that Obama is more popular among residents of the Jewish state than had been believed previously — but he’s still not all that well-liked. Forty-one percent of Israelis have favorable feelings toward Obama, with 37 percent expressing an unfavorable opinion of him, according to the poll, which had a margin of error of 3.1 percent.

But the poll also found that just 42 percent of Israelis believe Obama “supports Israel,” with 55 percent feeling that statement does not describe him. In addition, 43 percent said Obama is “naive,” and 39 percent said he is a Muslim.

The finding that 41 percent of Israelis have a favorable opinion of the president contrasts with a Jerusalem Post poll over the summer, often cited in the media, which found that just 4 percent of Israelis believed Obama’s policies are “pro-Israel.”

Obama’s favorable rating was higher than those garnered by Israeli Defense Minister Ehud Barak (30 percent) and Foreign Minister Avigdor Lieberman (38 percent), but lower than Israeli Prime Minister Benjamin Netanyahu’s 51 percent and two former presidents, Bill Clinton (59 percent) and George W. Bush (48 percent).

But 16 percent of the poll sample was Israeli Arabs. When only Jews are counted, Netanyahu and Bush’s favorable ratings jump respectively to 58 and 55 percent, with Clinton’s increasing by three points. Obama’s goes down a point.

Gil Tamary, a reporter for Israel’s Channel 10, pointed out that Obama’s approval rating of 41 percent was significantly lower than the 56 percent favorable rating that the United States received in the poll from Israelis.

He added that Clinton’s much higher popularity — even though he pushed “the same policies as President Obama” — demonstrated that Obama’s problem is “the way he handles the Israeli public.”

“We’re willing to make major concessions if you hug us and kiss us,” Tamary said. “If we get the cold shoulder, we’re giving the cold shoulder back.”

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