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Going by the numbers cited in a new national study, the Bay Area appears to have lost some 240,000 Jews. But who’s counting? And how?

In this case, it’s Brandeis University’s Steinhardt Social Research Institute and the Cohen Center for Modern Jewish Studies, which just published “American Jewish Population Estimates: 2012.”

The study puts the number of American Jews at a surprisingly robust 6.8 million, with 14 percent of them living in California. But it tallied the Bay Area’s entire Jewish adult population at just over 122,000, which would make it the nation’s 10th largest, behind cities such as Boston, Philadelphia and Washing-ton, D.C.

Source: American Jewish Population Estimates: 2012 Source: Pew Research Center 2013 Survey of U.S. Jews

That’s a far cry from the numbers cited in a 2004 demographic study commissioned by the S.F.-based Jewish Community Federation, and a similar one in 2011 from the Jewish Federation of the East Bay. Together, those surveys estimated the Bay Area Jewish population at approximately 360,000, which would place the region in the No. 3 or 4 spot nationwide.

So where did everybody go? It comes down to how — and whom — the studies count.

Brandeis social psychologist Leonard Saxe, director of the Cohen Center and the Steinhardt Institute, and one of the four authors of the new study, said the national population total included 4.2 million adults who consider Judaism their religion, nearly 1 million who identify themselves as Jewish by other criteria, such as ethnic or cultural, and approximately 1.6 million Jewish children.

The regional breakdowns, however, considered only the adults who identify Judaism as their religion (see chart above).

The team did not gather new data, but derived its numbers by analyzing existing data from more than 100 national population surveys, all of which used the standard demographer’s question, “What is your religion?”

“We’re confident that we have, with absolute precision, the number of adults who consider Judaism their religion,” Saxe told J.

He said if he were to adjust for secular Jews and children, using national averages, the total Jewish population of the Bay Area would be about 250,000 — still not close to the 360,000 the two local federations reported.

And the S.F. federation’s numbers are nearly 10 years old — surely there has been growth since then?

Bruce Phillips, who oversaw the 2004 San Francisco study, offered a few possible explanations for the numbers discrepancy. For one, he said, the Steinhardt-Cohen study had data only about the specific individuals interviewed, not anyone else who lived in the households.

“The [Steinhardt-Cohen] estimate comes from a meta-analysis of multiple surveys,” he said. “These surveys, unlike Jewish [community] surveys, do not ask the religion of every household member. Usually it’s only the respondent and sometimes the spouse.”

Phillips said the nature of the Bay Area Jewish community also affected the results of the new study.

“The Bay Area has a much higher proportion of Jews who don’t identify with Judaism,” he said. In his 2004 study, “You have 123,000 adults who identify with Judaism. Add another 60,000 Jewish adults who identify with no religion, or Buddhism or something like that.” In 2004, according to Phillips, the total number of Jews in the area served by the S.F. federation was 228,000, including children.

East Bay federation CEO Rabbi James Brandt said the East Bay’s 2011 study was commissioned for the purpose of better understanding the population his organization serves. That includes self-identified religious Jews, Jews who do not consider themselves religious, as well as non-Jewish spouses who, for example, light Shabbat candles with their children.

“The numbers we captured were the people who consider themselves affiliated in some way with the community,” Brandt said. “We found 100,000 adults who identify themselves as Jews, and 70,000 who identified as non-Jews living in Jewish households.” The study also found approximately 30,000 Jews who live in non-Jewish households, for a total of 130,000 Jewish individuals.

Brandt said it comes down to the age-old question: Who is a Jew?

“For the purposes of our study it was the self-identified Jew,” he added. “That includes cultural Jews who do not consider themselves affiliated, and also someone who has not officially converted.”

Saxe acknowledged that Bay Area Jews might well be underrepresented in a count that depends on them identifying as Jewish by religion. Asked how Boston came out ahead of the Bay Area in the Steinhardt-Cohen study, Saxe noted that synagogue affiliation is very high in Boston.

That means more Boston-area Jews are likely to identify with the religion than their counterparts on the famously unorthodox West Coast. “This is a reminder of how many Jews in the Bay Area identify in unconventional ways,” said Phillips. “Big surprise: The Bay Area Jewish community is different from northern New Jersey or Chicago.”

To read “American Jewish Population Estimates: 2012,” go to http://tinyurl.com/brandeis-jewish-study-2012.