If you are good at one intelligence task does it make you more likely to be good at most others (i.e., are intelligence tasks positively correlated to each other)?

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Yes! The positive manifold refers to the empirical observation that all cognitive ability tests tend to be positively correlated with each other meaning that individuals who perform well on one type of cognitive test (e.g., verbal reasoning, or math, or pattern finding) are also likely to perform well on most other types of cognitive tests (e.g., spatial reasoning, memory, or processing speed). Since we administered 62 different cognitive tests to our participants, we were able to calculate correlations between each pair of those tests. Out of 1891 pairwise correlations, 1847 (98%) were positive, while only 44 (2%) were negative. Furthermore, the absolute average value of positive correlations was much higher than the absolute average value of negative correlations (r = 0.42 vs. r = 0.07). Based on these results, we can be fairly certain about the positive manifold theory. The average correlation between all pairs of tasks was r=0.41.

Note: The phrase "positive manifold" in the field of psychometrics originally had a different meaning, but we're using the more commonly used modern meaning of the term.

Below is a nice illustration of this pattern that we produced from our data. Blue color denotes positive correlation, and the darker it is, the greater the correlation. Red means that the correlation is negative. Note how few red rectangles there are. The tasks are ordered by g-loading, with the highest g-loaded tasks first and the lowest last.

Of course, while we tested a very wide range of intelligence tasks (62 distinct tasks), we did not test every conceivable intelligence task. So there could be some intelligence tasks that have no correlation with the bulk of intelligence tasks. But we didn't find any like that. The intelligence task we used in our study that turned out to have the lowest average correlation to the other tasks still had a meaningfully average positive correlation with the other tasks (r=0.18).

It's also interesting to note that if we conduct principal component analysis on this matrix of task correlations, we find that the first principle component accounts for 45% of the variance, with a very sharp drop after that, as can be seen in the chart below:

This suggests that there was primarily one hidden factor accounting for performance across the tasks - though it doesn't rule out the possibility of other, substantially weaker factors. Note that the shape of this normalized eigenvalues plot, above, may be partially effected by our study design, which involved each study participant getting a small random sample of intelligence tasks (chosen from a much larger set of 62 tasks). For participants we recruited from Positly, they completed 7.7 tasks on average (a median of 7 tasks) selected at random from our full set of 62 potential intelligence tasks, whereas our non-Positly sample completed 5.9 tasks on average (median of 6 tasks).

What do the other studies say?

Although not all researchers agree on the ultimate explanation for the positive correlations between different cognitive tasks (i.e., positive manifold), studies generally agree that the positive manifold of cognitive tasks exists (e.g., Burgoyne et al., 2022; Jensen, 1986; Kovacs & Konway, 2016; Pluck & Cerone, 2021;  van der Maas et al., 2016).

In fact, it was this observation that almost all intelligence related tasks are positively correlated that makes the concept of measuring an IQ score potentially useful. If performance on different intelligence related tasks were all uncorrelated, it wouldn't make sense to assign a single score.

Takeaways

• There is a positive manifold of intelligence tasks, meaning that intelligence tasks are positively correlated to each other.

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