Are billionaires smarter than the average individual? A new report suggests they may well be.

Jonathan Wai, a research scientist at Duke University’s Talent Identification Program, a nonprofit organization that serves academically gifted and talented youth, says he’s found a correlation between wealth and intelligence.

“America’s elite are largely drawn from the intellectually gifted, with many in the top one percent of ability,” Wai writes in Investigating America’s Elite: Cognitive Ability, Education, And Sex Differences, to be published in the July-August issue of the journal Intelligence.

But not everyone is buying Wai’s conclusions. Some criticize the fact that his conclusions are based on what colleges his test subjects attended, with no consideration of each individual’s grades and test scores.

“Anybody can become wealthy in this country with the right ambition, the right focus, the right belief system and maybe a little luck,” says Steve Siebold, author of How Rich People Think.

To determine whether rich people are smarter, Wai examined the standardized test scores required for admission to ultra-selective colleges and graduate schools, such as Harvard and Yale. Wai says these test scores are a reasonable indicator of general intelligence.

Wai examined 2,254 individuals in five groups of America’s elite political and business leaders. His research found that about 45% of billionaires, 41% of senators, 41% of federal judges and 39% of Fortune 500 CEOs attended a school requiring test scores that likely puts them in the top 1% of ability. About 21% of the final category of elites, members of the House of Representatives, attended a school targeting the most capable 1%.

Billionaires who made their money from the investments sector were the most likely to have attended an elite school, followed by those who earned their money in the technology sector. Billionaires who got rich in real estate, services, energy, media, fashion and retail, as well as food and beverage, ranked lower in elite school attendance. The median billionaire net worth was $2.3 billion, compared to a median Fortune 500 CEO “total calculated compensation” of about $9.7 million.

Siebold, however, argues that formal education has little to do with how much wealth one can acquire. While the rich respect the value of being well schooled, they don’t usually associate it with building a fortune, he says.

“Many of the world's wealthiest people have little formal education and, in fact, many never completed high school or dropped out,” Siebold recently wrote in the Huffington Post. “The bottom line: Don't listen to these reports that say only intelligent people who received an Ivy League education can get rich.”

The study found that, “at least in 2012, Democrats were more likely than Republicans to have attended an elite school and to be in the top percentile of ability.” Women were underrepresented among all groups, but to a lesser degree among Democrats and federal judges, and to a greater degree among CEOs, Republicans and billionaires. The women who became Fortune 500 CEOs, although quite low in number, “were smarter and attended a more prestigious school than their male counterparts,” according to the study.

Wai told Private Wealth that he doesn’t have an explanation for the differing results based on political party affiliation or gender. He also says he would have preferred to have had individual test scores for the study. But, overall, he believes average scores are a valid measure of intelligence.

Wai’s study also notes that just because someone goes to a top-tier school, it doesn’t prove he or she is intellectually gifted. Many of these schools admit students who do not meet test score criteria based on other factors, such as having athletic ability or a family relation to alumni of the institution.

Wai acknowledges that his study has limitations when it comes to measuring achievement. “Certainly luck has a role to play. Social skills have a role to play. Motivation, drive, willingness to work really long hours—these are all important factors,” he says. “All I’m arguing is that intelligence is one factor in success.”