It took 18 years for DNA evidence to surface that cleared Derrick Williams of a rape and attempted kidnapping in Florida. Prosecutors had relied on the testimony of the victim, who identified Williams as her attacker in 1992. But he walked free at age 48 in 2011 because his DNA didn't match that left on a gray T-shirt by the actual perpetrator.

The truth might have surfaced sooner if Williams were white or Latino instead of African-American.

There's no way to know for sure, of course, but data about wrongful convictions show that blacks who are exonerated after a bogus conviction have served 12.68 years on average before the good news, according to Pamela Perez, professor of biostatistics at Loma Linda University. It takes just 9.4 years for whites and 7.87 for Latinos.

"Black Americans are exonerated at a substantially slower rate than any other race," said a new report from Perez, shown exclusively to The Huffington Post.

There's enough of a pattern that the differences between racial groups cannot be called random, Perez said. But there isn't enough information to explain what caused the differences. SUBSCRIBE AND FOLLOW Get the top stories emailed every day. Newsletters may offer personalized content or advertisements. Privacy Policy Newsletter Please enter a valid email address Thank you for signing up! You should receive an email to confirm your subscription shortly. There was a problem processing your signup; please try again later Twitter

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"All we can do is infer," Perez told HuffPost. "You can't prove a darn thing."

She discovered the different timespans by examining 1,450 exonerations listed on the National Registry of Exonerations through Oct. 20, 2014. Perez conducted the research for Safer-America.com, a consumer research group.

Safer-America translated the data into a map showing exoneration information across the U.S.

The findings are based on what is probably only a fraction of all exonerations. There are likely cases that didn't make it onto the national registry, and there are almost certainly more wrongly convicted people still waiting to clear their names.

The registry didn't collaborate with Perez, but one of its researchers reviewed Perez's work at HuffPost's request and approved of her methodology.

"I'm not surprised by the numbers," said Sam Gross, the exoneration registry's editor and a University of Michigan law professor. "The main thing we can say is that it's very hard to know what it means."

Perez, Gross and others cautioned against jumping to conclusions about the findings. Without further research, they said, no one knows if the results were caused by a biased criminal justice system or other factors.

The Innocence Project looked at a smaller set of 212 cases in which DNA proof freed their clients. (The national registry includes exonerations due to other contributing factors like false confessions and perjury.) The project found a similar racial disparity, with black inmates serving 14.3 years before being exonerated compared to 12.2 years for all other racial groups.

"The difference between these two numbers is statistically significant, suggesting that the difference between them isn't due to chance," Innocence Project research analyst Vanessa Meterko said in a statement. "This is notable, but it's hard to say what the reason for the difference is."