# Proof Narrative: The correlation between human brain volume and intelligence is r = 0.4

## Verdict

**Verdict: PARTIALLY VERIFIED**

The figure r = 0.4 is not simply right or wrong — it depends critically on what you're measuring and who you're measuring it in.

## What was claimed?

The claim is that brain size and intelligence are correlated at r = 0.4. This kind of figure shows up in textbooks, popular science articles, and debates about the biology of intelligence. If true as a general statement, it would mean bigger brains are meaningfully associated with higher IQ scores across the population — a modest but real relationship.

The number matters because it's often cited to support the idea that brain volume is a useful predictor of cognitive ability. An r of 0.4 is noticeably stronger than, say, 0.2, and the difference shapes how seriously the brain–IQ link gets taken in both science and public discourse.

## What did we find?

The picture splits into two distinct stories depending on which version of the question you're asking.

When researchers have pooled together every study they can find — regardless of sample quality, test type, or health status — the answer comes out consistently lower than r = 0.4. Two of the largest and most rigorous meta-analyses on record both converge on r = 0.24. One of these analyzed 88 studies covering more than 8,000 subjects; the other, more recent one covered 86 studies with over 26,000 participants. These were conducted by independent research teams using different statistical approaches, yet they landed on the same number. The unconditional correlation between brain volume and IQ is approximately 0.24, not 0.40.

That gap — 0.24 versus 0.40 — isn't a rounding difference. It's a substantive disagreement. And the evidence runs in only one direction: publication bias in this literature tends to inflate reported correlations, not deflate them. After correcting for the tendency of journals to publish studies with larger effects, the true unconditional correlation is likely at or below 0.24.

So where does r = 0.4 come from, and is it completely wrong? Not exactly. A separate body of work specifically examined what happens when you restrict the analysis to healthy adult samples and use the highest-quality, most g-loaded intelligence tests. Under those conditions — optimal measurement, optimal sample — the correlation does rise to approximately 0.40. This conditional result is backed by peer-reviewed research published in a specialist journal and is a credible scientific finding. It just doesn't apply to people in general.

The claim as stated gives no indication that r = 0.4 only holds under specific conditions. Read as a general fact about brain volume and intelligence, it overstates the relationship by a considerable margin.

## What should you keep in mind?

The distinction between r = 0.24 and r = 0.40 is entirely about how you sample and how you measure. Neither number is wrong in its proper context — the problem is using the conditional estimate as if it were the unconditional one.

It's also worth noting that even r = 0.24 is a real and statistically meaningful association; the evidence doesn't say brain size is irrelevant to intelligence. It says the relationship is weaker and more contingent than the headline figure suggests.

The Wikipedia source that supports the r = 0.40 figure is itself reliable — it accurately reflects the peer-reviewed literature on conditions under which the correlation reaches that level. The issue is context, not fabrication.

Finally, the largest modern meta-analysis found that effect sizes have been declining over time in this literature, which may reflect corrections for earlier methodological weaknesses or genuine changes in how samples are constructed.

## How was this verified?

This claim was evaluated by locating and cross-checking the major published meta-analyses on brain volume and IQ, computing the deviation of each reported estimate from r = 0.40, and explicitly testing whether publication bias could account for any gap. You can read the full evidence and reasoning in [the structured proof report](proof.md), inspect every citation and computation step in [the full verification audit](proof_audit.md), or [re-run the proof yourself](proof.py).