How this test is built and scored

Why these five item types

Decades of factor-analytic work converge on a small set of tasks that load heavily on general reasoning ability. Figural matrices are the classic example — they were the basis of Raven's Progressive Matrices and remain one of the purest available markers of fluid intelligence. Number series tap the same inductive process in a quantitative form, mental rotation adds the spatial dimension that broad-ability models treat as a distinct but correlated factor, and classification (odd one out) and figure analogies are the two other item formats that appear in almost every established non-verbal battery.

• Pattern matrices — Inductive reasoning — spotting rules that run across, down and diagonally through a grid.
• Number series — Quantitative reasoning — inferring the rule behind a run of numbers.
• Spatial reasoning — Spatial visualisation — telling a turned figure from a flipped one.
• Odd one out — Classification — finding the one figure that breaks the rule the others share.
• Figure analogies — Analogical reasoning — carrying a transformation from one pair over to another.

All items are non-verbal: none of them requires reading a sentence, and none depends on vocabulary. The figural items — matrices, rotation, classification and analogies — require no language and no cultural knowledge at all, so they travel well across languages. The number series are the exception. They need no language either, but they do assume ordinary arithmetic fluency: some turn on recognising square numbers, factorials or a doubling rule, and that is acquired mathematical knowledge. Sixteen of the seventy-two items in the bank are number series, so the test as a whole is not culture-free in the way the figural items are — if arithmetic is unfamiliar to you, that part of the test will understate your reasoning.

Difficulty weighting

Each item carries a difficulty rating from 1 to 5, and your score is the weighted proportion you answered correctly rather than a plain count, so a correct answer on a hard matrix moves your score more than a correct answer on the opening warm-up.

This is a deliberate design choice, not an approximation of item response theory — it is a departure from it. Under a Rasch (1PL) model the unweighted raw score is a sufficient statistic for ability: every item counts exactly once, however hard it is. The 2PL and 3PL models that do weight items weight them by discrimination, not difficulty; an item's difficulty parameter says where on the ability scale that item carries information, not what a correct answer to it is worth. We weight by difficulty anyway, because on a short test it separates the top of the range more sharply than a plain count does. That is the reason for the choice; the standard models are not.

Items are presented in ascending difficulty, interleaved across the five types so no single skill dominates one stretch of the test.

The item bank is larger than any single sitting. Each attempt draws one of three parallel forms, matched for content and difficulty but built from a different selection of items with the answer options in a different order. The forms are not fully disjoint, though, and the overlap matters if you retake the test. The three full forms share 14 to 15 of their 35 items, so a second full attempt re-shows roughly 40% of the items you have already seen, and a second score is inflated by both practice and recall. The three quick forms share only one to three items, so the quick test is much the better one to retake.

From answers to an IQ number

Your weighted proportion correct is converted to a z-score against the expected performance of an average adult on this item mix, then mapped onto the deviation IQ scale used by every modern test: a mean of 100 and a standard deviation of 15. Your percentile follows directly from the normal distribution.

The quick test carries fewer items, so it is slightly less reliable. Its estimate is shrunk a little toward the mean to avoid overstating extreme results from a short sitting. Because of that shrinkage, the quick test produces scores from about 66 to 137 and the full test from about 61 to 142; it does not report values beyond that range. For a plain-language walkthrough of the bands, see what is a good IQ score.

The two constants behind that conversion — an expected weighted proportion of 0.48 and a standard deviation of 0.185 — were not estimated from any sample. They are assumed starting values, chosen to place a typical adult near 100, pending a standardisation sample of completed sittings. Until enough sittings accumulate to replace them, the IQ figure is best read as a well-scaled percent-correct rather than as a norm-referenced score.

Alongside the number, every result carries a 95% interval. It is the binomial sampling error of a finite set of items: with only 20 or 35 questions, the proportion you got right is itself an estimate, and the interval (a Wilson score interval, carried through the same conversion) says how much the score could move if you sat an equivalent set of items instead. It narrows on the longer test, because more items mean less sampling error. Read it as a floor rather than a full margin of error — it captures only the item sampling, not error in the norms themselves, so the true uncertainty is wider than the interval shown.

A result that is not statistically distinguishable from guessing — fewer than 8 correct of 20 on the quick test, or fewer than 12 of 35 on the full test — is reported as being at chance level rather than as an IQ score, and is left out of the site-wide averages.

What this test cannot do

It is not a clinical instrument. Professional assessments such as the WAIS are administered one-to-one by a trained psychologist, take a couple of hours, and cover verbal comprehension, working memory and processing speed alongside reasoning. They are normed on large representative samples with careful age adjustment.

This test has no standardisation sample behind it: its scale rests on assumed constants rather than on measured norms, and it cannot control your environment, your sleep, or whether you have seen matrix puzzles before. Treat the number as an interesting estimate with a margin of several points either way — never as a diagnosis or a basis for any educational, medical or employment decision.

Retaking

Practice effects are real: second attempts on matrix-style tests typically rise a few points regardless of ability. Your first genuine attempt is the most informative one.