The new approach tests five big factors of personality-namely neuroticism, extroversion, openness, agreeableness, and conscientiousness-as well as their sub-factors.
So far, it has been used to make psychological assessments of all 41 US presidents prior to George W. Bush, and to rank them eight different types, from "dominators" to "actors".
More recently, the same tool was used to profile John McCain, Rudolf Guiliani, and Hillary Clinton. Unfortunately, the analysis did not include Barack Obama.
"There wasn't enough quality biography on him to do so," said lead researcher Steven Rubenzer, a forensic psychologist in Houston, Texas.
The researcher said that McCain scored strongly on the trait of "extraversion" compared with average scores of previous presidents, but he was below average on "agreeableness" and "conscientiousness".
Rubenzer further said that McCain also scored highly on "angry hostility", "impulsivity", "excitement seeking", "positive emotions" and "openness to feelings", but was low on "compliance" and "deliberateness".
"McCain is most similar to presidents classified as extraverts such as Franklin D Roosevelt, Theodore Roosevelt and John F Kennedy, and dominators, again including Theodore Roosevelt, and Andrew Jackson," the researcher said while presenting the findings at the annual meeting of the International Society of Political Psychology in Portland, Oregon, in July last year.
Both Guiliani and Hillary Clinton scored extremely low on agreeableness. On overall ratings, McCain came out best of the three.
"McCain shows the highest resemblance to a composite rating of better-that-average presidents. This may have been due to his higher extraversion than the other two," says Rubenzer.
In all, his team has found 240 items of measurement for each president, which enable them to work out which presidents were the "greatest" by comparing them against each other, a kind of peer-versus-peer test.
Rubenzer and colleagues found that the most important traits for true greatness were "openness", "assertiveness" (a sub-set of extraversion) and "achievement striving" (a subset of conscientiousness).
They further said that "conscientiousness" generally also emerged as a predictor of historical greatness, and Washington came out highest on that measure, and
Surprisingly, the best presidents also need to be haphazard, said the researchers.
"Being a bit disorganised, like Abraham Lincoln, is somewhat of an asset for attaining historical greatness," they said.
Rubenzer pointed out that perhaps the trait of most vital importance was "openness to experience", the ability to assimilate new values, emotions, feelings, and aesthetics.
According to the team, this trait also correlates most strongly with intelligence.
"Great presidents are attentive to their emotions, willing to question traditional values and try new ways of doing things, imaginative and more interested in art and beauty than less successful ones. Historically great, high-openness presidents include Jefferson and Lincoln," they say.