Positive manifold refers to the fact that scores on cognitive assessment tend to correlate very highly with each other, indicating a common latent dimension that is very strong.  This latent dimension became known as g for general intelligence or general cognitive ability.  This post discusses what the positive manifold is, but since there are MANY other resources on the definition, the post also explains how this concept is useful in the real world.

The term positive manifold originally came out of work in the field of intelligence testing, including research by Charles Spearman.  There literally hundreds of studies on this topic, and over one hundred years of research has shown that this concept is scientifically supported, but it is important to remember that it is just a manifold and not a perfect relationship.  That is, we can expect verbal reasoning ability to correlate highly with quantitative reasoning or logical reasoning, but it is by no means a 1-to-1 relationship.  There are certainly some people that can be high on one but not another.  But it is very unlikely for you to be in the 90th percentile on one but 10th percentile on another.

What is Positive Manifold?

If you were to take a set of cognitive tests, either separate, or as subtests of a battery like the Wechsler Adult Intelligence Scale, and correlate their scores, the correlation matrix would be overwhelmingly positive.  For example, look at Table 2-9 in this book.  There are many, many more examples if you search for keywords like “intelligence intercorrelation.”

As you might expect, related constructs will correlate more highly.  A battery might have a Verbal Reasoning test and a Vocabulary test; we would expect these to correlate more highly with each other (maybe 0.80) than a Figural Reasoning test (maybe 0.50).  Researchers like to use a methodology called factor analysis to analyze this structure and drive interpretations.

Practical implications

Positive manifold and the structure of cognitive ability is historically an academic research topic, and remains so.  Researchers are still publishing articles like this one.  However, the concept of positive manifold has many practical implications in the real world.  It affects situations where cognitive ability testing is used to obtain information about people and make decisions about them.  Two of the most common examples are test batteries for admissions/placement or employment.

Admissions/placement exams are used in the education sector to evaluate student ability and make decisions about schools or courses that the student can/should enter.  Admissions refers to whether the student should be admitted to a school, such as a university or a prestigious high school.  Examples of this in the USA are the SAT and ACT exams.  Placement refers to sending students to the right course, such as testing them on Math and English to determine if they are ready for certain courses.  Both of these examples will typically test the student on 3 or 4 aspects, which is an example of a test battery.  The SAT discusses intercorrelations of its subtests in the technical manual (page 104).  Tests like the SAT can provide incremental validity above the predictive power of high school grade point average (HSGPA) alone, as seen in this report.

Employment testing is also often done with several cognitive tests.  You might take psychometric tests to apply for a job, and they test you on quantitative reasoning and verbal reasoning.

In both cases, the tests are validated by doing research to show that they predict a criterion of interest.  In the case of university admissions, this might be First Year GPA or Four Year Graduation Rate.  In the case of Employment Testing, it could be Job Performance Rating by a supervisor or 1-year retention rate.

Why are they using multiple tests?  They are trying to capitalize on the differences to get more predictive power for the criterion.  Success in university isn’t due to just verbal/language skills alone, but also logical reasoning and other skills.  They recognize that there is a high correlation, but the differences between the constructs can be leveraged to get more information about people.  Employment testing goes further, and tries to add incremental validity by adding other tests that are completely unrelated but relevant to the job world, like job samples or even noncognitive tests like Conscientiousness .  These also correlate with job performance, and therefore help with prediction, but correlate even lower with measures of g than another cognitive test would; this then adds more prediction power.

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Nathan Thompson, PhD

Nathan Thompson earned his PhD in Psychometrics from the University of Minnesota, with a focus on computerized adaptive testing. His undergraduate degree was from Luther College with a triple major of Mathematics, Psychology, and Latin. He is primarily interested in the use of AI and software automation to augment and replace the work done by psychometricians, which has provided extensive experience in software design and programming. Dr. Thompson has published over 100 journal articles and conference presentations, but his favorite remains https://scholarworks.umass.edu/pare/vol16/iss1/1/ .
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