As they reel from a succession of defeats in courtrooms and legislatures, opponents of same-sex marriage have a new chance this week to play one of their most emotional and, they hope, potent cards: the claim that having parents of the same sex is bad for children.

In a federal court in Detroit starting Tuesday, in the first trial of its kind in years, the social science research on family structure and child progress will be openly debated, with expert testimony and cross-examination, offering an unusual public dissection of the methods of sociology and the intersection of science and politics.

Scholars testifying in defense of Michigan’s constitutional ban on same-sex marriage aim to sow doubt about the wisdom of change. They brandish a few sharply disputed recent studies – the fruits of a concerted and expensive effort by conservatives to sponsor research by sympathetic scholars – to suggest that children of same-sex couples do not fare as well as those raised by married heterosexuals.

That view will be challenged in court by longtime scholars in the field, backed by major professional organizations, who call those studies fatally flawed. These scholars will describe a near consensus that, other factors such as income and stability being equal, children of same-sex couples do just as well as those of heterosexual couples.

"The overwhelming evidence so far is that there’s not much difference between children raised by heterosexual or same-sex parents," Andrew J. Cherlin, a prominent sociologist of family issues at Johns Hopkins University who is not involved in the case, said in an interview.

The last time these issues were debated in a federal court, in California nearly four years ago, social science opponents of same-sex marriage underwent withering challenges in pretrial depositions and did not even appear in court.

As he struck down Proposition 8, the California amendment limiting marriage to a man and a woman, Judge Vaughn R. Walker of U.S. District Court in San Francisco said he had heard "no reliable evidence that allowing same-sex couples to marry will have any negative effects on society."

For some conservatives, that decision amounted to a call to arms.

In meetings hosted by the Heritage Foundation in Washington in late 2010, opponents of same-sex marriage discussed the urgent need to generate new studies on family structures and children, according to recent pretrial depositions of two witnesses in the Michigan trial and others. One result was the marshaling of $785,000 for a large-scale study by Mark Regnerus, a meeting participant and a sociologist at the University of Texas who will testify in Michigan.

The trial involves a challenge to Michigan’s constitutional restriction of marriage to a union between a man and a woman, brought by a lesbian couple who want to marry and legally adopt each other’s children.

This time, four social science researchers, all of whom attended at least one of the Heritage Foundation meetings and went on to publish new reports, are scheduled to testify in favor of Michigan’s ban.

The most prominent is Regnerus. His study, published in 2012, was condemned by leading social scientists as misleading and irrelevant, but some conservatives call it the best of its kind and continue to cite it in speeches and court cases.

In other recent cases, judges were content to read the evidence in written briefs. But Judge Bernard A. Friedman of U.S. District Court in Detroit ruled that a trial was needed to determine whether the state had any legitimate reasons to discriminate.

Among those at the Heritage meetings was Luis E. Tellez, president of the Witherspoon Institute, a religious-conservative research center in Princeton, N.J. His organization seized the baton, signing up Regnerus, who was known as a skilled quantitative researcher, mainly on adolescent sexuality and religion, and as a Roman Catholic and opponent of same-sex marriage.

The institute gave Regnerus $695,000; the Bradley Foundation, a grant-making organization that supports conservative causes, gave him $90,000, according to his risumi.

Tellez did not reply to repeated requests for comment, but in a 2011 letter to the Bradley Foundation imploring it to support the study, he wrote that "time is of the essence," an apparent reference to the likelihood that same-sex marriage would soon reach the Supreme Court.

He added that his group was "confident that the traditional understanding of marriage will be vindicated by this study so long as it is done honestly and well." The letter was obtained through a public records request to the University of Texas by The American Independent, an investigative news site.

A chief charge by the opponents of same-sex marriage is that nearly all existing studies of gay parenting involved small, nonrandom samples, often of upper-income parents. Regnerus, in contrast, queried about 3,000 young adults, including 248 who reported that one of their parents had a homosexual relationship at some point.

He found that the subjects in that category fared worse based on a host of behavioral and psychological measures than those who grew up in intact traditional families. The study, Regnerus wrote, "clearly reveals" that children are most apt to succeed when they grow up "with their married mother and father."

The report appeared in Social Science Research, a respected journal that became embroiled in controversy after many experts questioned its editorial decision. The study was quickly trumpeted by conservative groups and has been cited in repeated court cases.

Regnerus has often spoken out against same-sex marriage and, in his pretrial brief to the Michigan court, wrote that "it remains prudent for government to continue to recognize marriage as a union of a man and a woman, thereby promoting what is known to be an ideal environment for raising children."

Heritage Foundation officials declined to offer details on the 2010 meetings and referred questions about research to Ryan T. Anderson, a doctoral candidate in political philosophy and fellow at the foundation who writes about marriage and religious liberty.

Anderson praised the Regnerus study and another sharply disputed report on high school graduation rates from Canada by Douglas W. Allen, an economist at Simon Fraser University in British Columbia who attended the 2010 Washington meetings and will be a witness in Michigan. Both reports, Anderson said, were "consistent with 40 years of rigorous social science showing that children tend to do best when raised to maturity by their biological, married mother and father."

Professional rejections of Regnerus’ conclusions were swift and severe. In a friend-of-the-court brief to the Supreme Court last year in two same-sex marriage cases, a report by the 14,000-member American Sociological Association noted that more than half the subjects whom Regnerus had described as children of "lesbian mothers" and "gay fathers" were the offspring of failed opposite-sex marriages in which a parent later engaged in same-sex behavior, and that many others never lived with same-sex parents.

"If any conclusion can be reached from Regnerus’ study," the association said, "it is that family stability is predictive of child well-being."

Wendy D. Manning, a professor of sociology at Bowling Green State University in Ohio and the main author of the association report, said of the wider literature: "Every study has shortcomings, but when you pull them all together, the picture is very clear. There is no evidence that children fare worse in same-sex families."

More research is needed as society changes, but it cannot guide marriage policy, she said, noting that only about half the children in the United States live with married, biological parents.

Children of single mothers, adopted children, children of divorce and children in poverty all have worse outcomes on average than children in stable middle-class marriages.

"Are we going to hold same-sex parents to a different standard than heterosexuals?" she asked.

Erik Eckholm, New York Times

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