WASHINGTON — When the Supreme Court considers on Tuesday whether hundreds of thousands of women can band together in an employment discrimination suit against Wal-Mart, the argument may hinge on the validity of the hotly disputed conclusions of a Chicago sociologist.

Plaintiffs in the class-action suit, who claim that Wal-Mart owes billions of dollars to as many as 1.5 million women who they say were unfairly treated on pay and promotions, enlisted the support of William T. Bielby, an academic specializing in “social framework analysis.”

A central question in the case is whether he should have been allowed, in preliminary proceedings, to go beyond describing general research about gender stereotypes in the workplace to draw specific conclusions about what he called flaws in Wal-Mart’s personnel policies.

“Bielby made a conclusion that he had no basis to make,” said Laurens Walker, one of two University of Virginia professors who coined the term for the analysis almost 25 years ago. “He hasn’t done the research.”