How the score is computed

1 · What the test contains

Rounds run in a fixed order — reasoning first while attention is freshest, speed last because it is the least g-loaded and the most robust to fatigue. The order is not randomised, so fatigue is the same for everyone.

Weighting

Equal weighting would let processing speed move the headline number as much as fluid reasoning, which is not defensible: fluid reasoning has a g-loading around .80 and processing speed around .50. The weights above approximate typical published loadings. They are a reasoned choice, not an empirical result.

Item construction

Four of the five domains generate their items programmatically from rule families — matrix completion, number series, digit sequences, and symbol streams — from a fixed seed, so the item set is identical for everyone and reproducible from the source. Verbal analogies are hand-authored; 24 exist so weak items can be swapped out without rebuilding the round.

Difficulty is designed rather than emergent. Each slot has a target proportion-correct, and distractors are built so each is wrong for a different reason — otherwise an item rewards elimination instead of reasoning.

2 · Raw scores to IQ

Step 1 — domain z-scores

z = (raw − μ) / σ, using the reference figures in section 3.

Step 2 — weighted composite

c = 0.30·z_fluid + 0.25·z_quant + 0.20·z_verbal + 0.15·z_memory + 0.10·z_speed

Step 3 — the correction that matters

A weighted sum of correlated z-scores does not have SD 1. Cognitive domains intercorrelate at roughly ρ = .50, and with these weights:

Var(c) = Σwᵢ² + ρ·Σᵢ≠ⱼ wᵢwⱼ = 0.225 + 0.50(0.775) = 0.6125, so SD(c) = 0.783.

Dividing by 1.0 instead of 0.783 inflates every deviation by about 28% — someone whose true score is 115 gets shown 119, and someone at 130 gets shown 138. This is the single most common defect in online IQ tests, and it flatters everyone, which is presumably why it survives.

IQ = 100 + 15 · (c − μ_c) / σ_c

Step 4 — interval and range

Composite reliability is estimated at 0.85 for a battery this length, giving SEM = 15 × √(1 − 0.85) = 5.81 and a 95% interval of about ±11 points.

Displayed scores are clamped to 55–145, roughly ±3 SD. The uncapped value is shown in the working, but around 31 rounds of items genuinely cannot distinguish between scores further into the tail than that. Any short test reporting a confident 160 is inventing the number.

3 · Where the reference figures come from

This is the part to read sceptically, because it is the weakest link in the whole model.

Published norms are expressed in scaled scores and cannot legitimately describe “correct out of 8 on these particular matrices”. So the distribution’s shape is borrowed from psychometric convention — normal, SD 15 — while the raw-score parameters are derived from the designed difficulty of the actual items:

μ = Σpᵢ and σ = √(Σpᵢ(1−pᵢ)) × 1.35, where pᵢ is each item’s target proportion-correct and the 1.35 factor inflates for inter-item correlation.

Processing speed is the one domain with a real external anchor: digit-symbol substitution tasks run around 55 correct in 90 seconds for adults, which scales to about 35 at 60 seconds. The rest are construction estimates.

4 · What happens to your data

Nothing, because none is collected. There is no database attached to this site.

While you are taking the test, a signed cookie holds one number per completed round — your score for it, nothing else. The answer key stays on the server, which is why each round is graded there rather than in your browser.

At the end, your whole result is encoded into the result link itself and signed. That is why a shared link opens for anyone and still works months later with no account: the page rebuilds the result from the URL. The signature is there so nobody can edit their score upward before sharing it.

5 · Limitations, stated plainly

The reference distribution is constructed, not observed

Covered above, and it is the big one. Every figure in that table comes from how the items were designed rather than from watching people answer them. If the items turned out harder or easier in practice than intended, every score shifts with them, and there is no feedback loop to catch it.

Reliability is estimated, not measured

The 0.85 figure driving every confidence interval is a reasoned estimate for a battery of this length. Measuring it properly would need a stored response sample, which this site deliberately does not keep. The intervals are approximately right rather than exactly right — and an approximately right interval still beats a confident point estimate.

Two domains are technically cheatable

Digit span has to send the digits to your browser to display them, and the symbol key has to be visible to be usable — so in both cases a determined person could script the answer. That is inherent to running these tasks in a browser, and it is one reason those two carry the lowest weights (0.15 and 0.10). The three highest-weighted domains keep their answer keys on the server.

Everyone sees the same items

One fixed item set, so raw scores stay comparable to the reference figures. The cost is that the items can be memorised, and a retake shows the same ones. Practice will inflate a second attempt; the first is the meaningful one.

Verbal reasoning is culture-loaded

Analogies test relational reasoning through vocabulary, which means they also test vocabulary — and therefore language background and education. That is why verbal carries 0.20 rather than more, and why a low verbal score on an otherwise high profile is worth reading as a language signal before an ability one.

Fifteen minutes is fifteen minutes

A clinical battery runs 60–90 minutes with a trained administrator, partly for reliability and partly to notice when something other than ability is affecting performance — fatigue, anxiety, a misread instruction. This test cannot do that. The confidence interval is the honest expression of what a short unsupervised test can claim.