There is considerable psychological consensus on how to go about measuring the psychological trait called IQ. There is less consensus about how to measure creativity, and even the lay meaning of the term often starts to break down when one tries to find the devil in the details.
There are multiple dimensions to the psychological and psychometric construction of "creativity" that are contentious.
One addressed in a recent post at Marginal Revolution, is whether creativity is a general trait, or a domain specific one. Maybe there is no relationship at all between verbal creativity and visual creativity, for example. The evidence cited in the post suggests that creativity may be domain specific (although an alternate hypothesis would be that it was a general trait that only expresses well in combination with other traits like verbal or visual aptitudes).
Another dimension, not discussed in the post, is whether creativity has more to do with the originality of one's ideas, or one's output of ideas, even if most of those ideas are mediocre, or at least, unexceptional.
The Johnson O'Connor Foundation, for example, which focuses on psychometrics, originally as a personnel management tool and more recently with an eye towards career counseling, calls its creativity test a measure of "Ideaphoria", i.e. raw volume of idea output. The operational test they used for the trait involved (maybe it still does) writing down as many responses as possible to a prompt in a set time period - the more responses one writes, the higher the score.
Other common tests, such as one often used to determine if someone is eligible to enter a gifted and talented program that is seeking to be inclusive of creative talent, try to measure divergent thinking rather than idea volume, and one of the most common ones arguably blends to separate traits in an incoherent way:
Efforts to assess creativity have been plagued by supposedly domain-general divergent-thinking tests like the Torrance Tests of Creative Thinking, although even Torrance knew they were measuring domain-specific skills. (He create two different versions of the test, one that used verbal tasks and another that used visual tasks. He found that scores on the two tests were unrelated —they had a correlation of just .06—so they could not be measuring a single skill or set of skills. They were—and still are—measuring two entirely different things.)
Of course, when a measurement tool used widely in research and application is deeply flawed, it can put a damper on the credibility of the entire undertaking, extracting systemic degradation in the quality of the work done across the field. It is a classic case of the perils of academic group think. Criticisms of other widespread psychological constructs used to operationalize ideas like personality and deviance consistently (e.g. the Five Factor Model of personality, and the DSM-IV), have some of these concerns at their root.
The Johnson O'Connor Foundation focused on idea volume rather than divergent thinking based upon the observation that idea volume was more consistently linked to professions commonly considered to be "creative professions" than other measures of creativity based on divergent thinking.
It also observed that lack of "ideaphoria" (like most personality traits) isn't necessarily a bad thing. Creativity can be a hindrance in vocations where consistency and "steadiness" are virtues like dentistry or accounting or managing a stable organization. Interestingly, it found that sales was a field where extroversion and creativity were both critical, while vocabulary (a good proxy for education and IQ), which was important in economic success in almost every other field didn't matter much. They also identified a "group influencing" cluster of personality traits (extroversion, creativity, and high reasoning ability) associated with professions, like teaching and politics, that revolve around influencing groups of people in public forums.
Many top talents in creative fields, Shakespeare, for example, are notorious for using immense amounts of borrowed or derivative material and breathing new life into it, while stage actors and musicians, often are tasked with bringing only new nuance into a predetermined and tightly determined sequence of dialog lines or musical notes invented by someone else.
Similarly, while most people consider reasoning ability to be a good thing, low levels of the trait were valuable in fields where insisting on evidence rather than inferrence is important, and where the systems one deals with are too complex to reduce to systemic rules.
Studies that have looked at "plus factors" that influence real world success after controlling for IQ, have largely focused on variants on the Big Five traits of conscientiousness and extroversion. The former sometimes gets described as "attention to detail", being a "self-starter", "self-discipline," being hard working and diligent as opposed to lazy, and having "grit." The latter is sometimes expressed in terms of having "people skills," having "empathy" or "emotional intelligence," being "energetic", being a "team player," and being a good "networker." But, creativity hasn't received as much systematic study, in part due to a lack of a definitional consensus about how to model it psychologically.
Of course, the perennial nature v. nurture debate also comes out in the discussions of the psychology of creativity. Is creativity something you are born with, or is it something that you develop with practice and even training? A domain specific creativity construct favors thinking of creativity as a form of "expertise" not just in the sense that it is not general to all fields, but also in the sense that it is acquired rather than inborn.
For example, are great composers distinguished by their great musical talent, that opens up the door to more possibilities to them than to lesser lights, or by a genuinely greater flow or more innovative flow of ideas?
Often ideas flowing from broader experience can look creative to people who don't have the same experiences, even if the person with the ideas doesn't have more or different ideas than someone with similar experiences. Patent law, for example, talks about inventions that are not obvious to people skilled in the field where the innovation takes place, even if they would be non-obvious to a non-expert. Similarly, when a chess master makes what looks like amazingly creative moves, this often has more to do with simply having a greater repertoire of options in the master's experience to draw from than from innovation, per se. A personal trainer who memorized more different exercises may look more creative than one who does not, because the personal trainer who knows more exercises can vary a routine more easily.
Given that greatly knowledge and experience and expertise in a domain can "look creative" the question then is whether once that effect is stripped away, there is any meaningful residual of a personality trait called "creativity" that is left, and if so, what that diminished psychological construct that is still left with some kind of meaning amounts to at that point.