The analysis was presented during a federal court hearing last week in Philadelphia in a suit brought by the American Civil Liberties Union against Attorney General Alberto Gonzales and obtained on Monday by the Mercury News.

The ACLU said the analysis, by Philip B. Stark, a professor of statistics at the University of California, Berkeley, did not appear to substantially help the Department of Justice in its effort to prove that criminal penalties are necessary to protect minors from exposure to sexually explicit information on the Internet.

The Justice Department had commissioned the study as part of an effort to resurrect the Children's Online Protection Act, which was signed by President Clinton in 1998, but immediately challenged by the ACLU.

A federal district court in Philadelphia and a federal appeals court found the law to be unconstitutional. In June 2005, the Supreme Court upheld the ban on enforcement of the law but sent the case back to district court for more fact-finding regarding Internet filters.

"One of the things we think came out of the government's study is that the chance of running into graphic content on the Web when filters are on is extremely low," said Catherine Crump, staff attorney at the American Civil Liberties Union.

Stark's study found that only 6 percent of all queries returned a sexually explicit Web site, despite the consistent popularity of queries related to sex. It also found that the filters that did the best job blocking sexually explicit content also inadvertently blocked lots of content that was not explicit.

Government witnesses argued that while the percent of sexually explicit Web pages was small, it still amounted to a huge number. "A lot of sexually explicit material is not blocked by filters," Stark wrote in the conclusion to his study.

Attorneys for the Justice Department were not available for comment on Monday afternoon.

The eight-year-old lawsuit ignited widespread public debate last year after Google objected to a subpoena it had received to turn over billions of Web site addresses and two months of search queries to government attorneys. Google argued in federal court that the request would put both the private queries of Google users and the Mountain View, Calif., giant's trade secrets at risk.

A federal judge subsequently ordered Google to turn over 50,000 random copies of Web pages from its index, but did not require Google to produce search-engine queries. Microsoft's MSN and Yahoo provided a sample of 1 million Web sites. MSN, Yahoo and AOL also provided a week of search queries.

Seth Finkelstein, a programmer and civil-liberties activist, said Google's stance was "horribly self-serving."

"There were no privacy implications in the sense that the data was restricted to a very small set of researchers who were under various sets of protective orders," Finkelstein said.

Finkelstein said Stark's findings about the prevalence of pornography on the Internet are similar to other academic studies.

"What we are learning about the Internet is that it reflects life and that the Internet is not _ contrary to what some people might think _ more sexual than people are in general."

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