What a matrix reasoning item looks like
A typical item is a 3 by 3 grid of figures with the bottom-right cell empty, and six to eight answer options underneath. Some easier items use a 2 by 2 grid, or a single larger pattern with a piece cut out. Nothing has to be read or known: the task is to work out what changes across the rows and down the columns, and to pick the only option that obeys every change at once.
The difficulty comes from the number of rules acting together and how hidden they are. Easy items have one obvious rule, such as "the shape gets darker". Hard items combine three or four rules on different elements of the same figure, so you have to keep several hypotheses in mind while you check them. That load on working memory is a large part of what the item measures.
Where matrix tests come from
The British psychologist John C. Raven published the first Progressive Matrices in 1938: 60 items in five sets of 12, each set starting easy and becoming harder. Coloured and Advanced versions followed for children and for high-ability adults, and a modernised edition appeared in 2018. Raven wanted a test of reasoning that did not depend on reading or vocabulary.
David Wechsler's adult scale added a Matrix Reasoning subtest in its third edition (WAIS-III, 1997), and the children's WISC followed. In the current WAIS-5 it belongs to the Fluid Reasoning index alongside Figure Weights. Mensa admission sessions in many countries also use matrix tests. Our Mensa-format test and IQ test are modelled on the format of these tests, using original items.
The rules behind matrix items
A 1990 analysis of Raven's Advanced Progressive Matrices by Carpenter, Just and Shell found that nearly all items use a small set of rules:
- Constant in a row: an attribute stays the same across a row and changes between rows.
- Progression: an attribute changes by a fixed step, such as size growing or a shape rotating 90 degrees.
- Addition or subtraction: the third figure is the first plus or minus the second.
- Distribution of three: three values (for example circle, square, diamond) each appear once in every row and column.
- Distribution of two: two values appear in a row and the third cell is blank for that attribute.
Knowing the list does not make hard items easy, because you still have to find which rule applies to which element, but it explains why matrix tests feel familiar once you have done a few.
Why psychologists rely on matrix items
Matrix tests correlate strongly with the general factor g that runs through all mental ability tests, and they do it without language. That makes them useful for people tested in a second language and for comparisons across countries. They are not culture-free, though. Familiarity with abstract shapes and with timed tests helps, and the largest Flynn-effect gains of the 20th century, well above the overall average of about 3 points per decade, were found on Raven-type tests. See fluid vs crystallized intelligence for what this kind of reasoning is.
Matrix reasoning vs figure weights
Both are fluid-reasoning subtests on the Wechsler scales. Matrix Reasoning asks you to find a visual rule in a grid. Figure Weights shows balance scales with coloured shapes and asks which option keeps the last scale balanced, so it adds quantitative reasoning, close to solving simple equations with pictures. Figure Weights was introduced with the WAIS-IV in 2008. People who are strong in mathematics often find it easier than matrices; people with strong visual reasoning sometimes find the reverse.
How to approach a matrix item
- Look at one row first and name what changes: shape, fill, size, number, position, rotation.
- Check the same changes down the columns.
- Form your answer before looking at the options, then find it. Options are designed to match all but one rule.
- If two options still fit, look for a second rule you missed, often rotation or count.
- Do not spend too long on one item; timed tests reward moving on.
Practice makes the format familiar and can raise scores by a few points, but that gain reflects familiarity, not a change in ability.
Sources
Raven, J. C. Progressive Matrices: A Perceptual Test of Intelligence. H. K. Lewis, 1938.
Carpenter, P. A., Just, M. A. and Shell, P. "What one intelligence test measures: a theoretical account of the processing in the Raven Progressive Matrices Test". Psychological Review, 1990.
Wechsler, D. WAIS-IV Technical and Interpretive Manual. Pearson, 2008.
Flynn, J. R. "Massive IQ gains in 14 nations". Psychological Bulletin, 1987.
Frequently asked questions
What is matrix reasoning?
The ability to identify the rules in a grid of shapes and choose the piece that completes the pattern. It is a core measure of fluid intelligence and appears in most IQ tests.
What is a matrix reasoning test?
A test made up of pattern-grid items of increasing difficulty, usually timed. Raven's Progressive Matrices is the best-known example; the Wechsler scales include a Matrix Reasoning subtest.
What is matrix reasoning on the WAIS?
A subtest in which you see an incomplete grid or pattern and choose the missing piece from five options. It was added in the WAIS-III and sits in the Fluid Reasoning index of the WAIS-5.
What is the difference between matrix reasoning and figure weights?
Matrix reasoning asks for a visual rule in a pattern; figure weights asks which shapes balance a scale, adding a quantitative element. Both measure fluid reasoning on the Wechsler scales.
Can I take a Raven matrices test online?
The official Raven's tests are sold to qualified professionals and are not legitimately available free online. Online matrix tests, including ours, are modelled on the format with original items.
Can you get better at matrix reasoning?
Practice makes the format familiar and usually adds a few points, mostly in the first sessions. Research does not show that this carries over into general reasoning ability.