Raven's Progressive Matrices Explained

What a matrix item looks like

A matrix item shows a 3×3 (sometimes 2×2) grid. Eight cells are filled with figures that follow one or more rules across the rows and down the columns; the ninth is blank. Below the grid are six or eight answer options, one of which obeys every rule at once. The rules are never explained — discovering them is the task.

The items are “progressive” in two senses: they get harder through the set, and the rules stack. Early items need one rule (a shape moves one step to the right per cell). Late items combine three or four (the shape moves, its fill alternates, the count increases by one, and the third column is the first two columns combined).

The rules behind the puzzles

Analyses of Raven's item bank (notably by Carpenter, Just and Shell in 1990) found that almost every item can be described by a short list of rule types:

• Constant in a row — one attribute stays the same across the row.
• Quantitative progression — size, count or position changes by a fixed step.
• Distribution of three — three values of an attribute each appear once per row and once per column (a Latin square).
• Figure addition or subtraction — the third cell is the first two overlaid, or one removed from the other.
• Distribution of two — two of three values appear per row; the third is absent.

Harder items are harder for a measurable reason: they require more rules to be held in working memory at once, and they use rules (distribution of two, figure subtraction) that are less obvious than progression. That is why matrix tests correlate so strongly with working-memory capacity. The six puzzle types in our Mensa-style test map directly onto this list: position and direction, fill and alternation, rotation and reflection, size and count, combination rules, and Latin squares with conditional rules.

The three versions of Raven's test

Version	Items	For whom
Coloured Progressive Matrices (CPM)	36	Children 5–11, older adults, clinical use
Standard Progressive Matrices (SPM)	60 in five sets	General population, ages 6 to adult
Advanced Progressive Matrices (APM)	48 (12 + 36)	Adults of above-average ability; selection and research

The SPM was used by the British Army in the Second World War to screen recruits regardless of schooling, which is how it became the default “culture-reduced” test worldwide. The APM was built to separate people at the top end, where the SPM runs out of hard items — the same ceiling problem we discuss in how rare an IQ of 140 is.

What Raven's measures — and what it does not

Raven's loads very highly on the general factor g (see what the g factor is): in most factor analyses it is among the best single indicators of general intelligence available. It measures fluid reasoning almost exclusively, which is its strength and its limit. It says nothing about vocabulary, verbal comprehension, arithmetic fluency or processing speed, and a person with strong verbal and weak spatial abilities will score below their full-scale IQ on it.

Because the test needs no language, it has been normed in dozens of countries and used to track the Flynn effect; matrix scores rose faster over the twentieth century than vocabulary scores did. It is also the test most sensitive to practice on the specific item format, which is why Mensa and other bodies do not accept a Raven's score the candidate obtained online.

Matrix items in modern IQ tests

Wechsler added a Matrix Reasoning subtest to the WAIS in 1997 and to the WISC in 2003; the Stanford-Binet 5 and the Woodcock-Johnson have equivalents. Online tests use matrices for a practical reason as well: they can be generated by a program from a rule set, so every test taker can get different items and the answer key never has to leave the server. That is how the Fast & Accurate IQ test on this site works — the same test in all 20 languages, because there is nothing to translate.

Frequently asked questions