Visuospatial representations and reasoning

We have a paper coming out (Fugard, Stewart, & Stenning, to appear) relating performance on the visuospatial Raven’s Advanced Progressive Matrices items, as determined by DeShon, Shah, and Weissbein (1995), to position on the sub-clinical autism spectrum, measured by the Autism-Spectrum Quotient.  The more you report having autistic traits, the better you are at the visuospatial items.  This result fits nicely with the enhanced perceptual processing theory of autism.  It also provides more evidence that Raven’s matrices load highly on g because the test is a package of many kinds of intelligence test.

The forthcoming QJEP paper by Borst and Kosslyn pinged my radar as they use DeShon and colleagues’ classification of the Advanced matrices to further clarify the representations involved in visual imagery tasks.  In brief, their main task requires participants to remember a two-dimensional array of dots.  The dots are removed and an arrow appears.  Participants are then asked whether or not the arrow points at one of the locations previously showing a dot.  The task is neat: for trials where the arrow is pointing at one of the dot locations, and when participants give the correct answer, the distance from arrow to dot is proportional to the response time.  This is consistent with a model of visuospatial representation which requires sequential scanning analogous to what one would do with one’s eyes if the array were still visible.

Back to the visuospatial items of the Raven: correlations were nearly .5 with performance on the dot-arrow task, compared to .04 between the dot-arrow task and Raven’s verbal-analytic items.

There were also correlations between paper form board and paper folding tasks, and visuospatial items (.42 and .52, respectively) again weaker (and p > .05) for the verbal-analytic items (.23 and .24).

Now, what’s the best way to come up with a process model of what’s going on in all of these tasks?  I think work by Maithilee Kunda for Raven’s matrices is very promising.  She and colleagues are coming up with algorithms which operate directly on the visual images in the Raven’s test.  These algorithms tend to work best for the visuospatial items.  A big challenge is to get such algorithms to work across a range of different tasks and to use the algorithms to generate new psychological tasks and predictions.


Borst, G. and Kosslyn, S. M. (in press). Individual differences in spatial mental imagery. The Quarterly Journal of Experimental Psychology.

DeShon, R. P., Chan, D., & Weissbein, D. A. (1995).  Verbal overshadowing effects on Raven’s Advanced Progressive Matrices: Evidence for multidimensional performance determinants. Intelligence, 21, 135-155

Fugard, A. J. B., Stewart, M. E., and Stenning, K. (to appear).  Visual/verbal-analytic reasoning bias as a function of self-reported autistic-like traits: a study of typically developing individuals solving Raven’s Advanced Progressive Matrices. Autism.

Raven’s Advanced Progressive Matrices item taxonomies

There are classifications galore.  Below is a comparison of one by DeShon, Chan, and Weissbein (1995) with one by Styles (2008):

DeShon et al
Styles ? Analytic Both Either Visual
? 1 0 0 0 0
D/T 0 1 0 0 0
Distribution 0 2 0 0 0
Equation 0 1 3 0 8
S/D 0 1 0 0 0
S/D/T 0 3 1 0 0
S/T 0 0 0 0 1
Seriation 0 1 2 4 3
Transformation 0 3 0 0 1

Pretty good agreement between DeShon and co’s “visuospatial” and Styles’ “equation” (both what does and doesn’t fall into these buckets).  The “equation” items concern those with “overlapping elements” – seems pretty visuospatial.  Also neither classification codes item 15: DeShon and co say it violates the task instructions.  The rest is a bit of a mess, but then Styles peeked at a higher resolution into the analytic items.


DeShon, R. P., Chan, D., & Weissbein, D. A. (1995).  Verbal overshadowing effects on Raven’s Advanced Progressive Matrices: Evidence for multidimensional performance determinants. Intelligence, 21, 135-155

Styles, I. (2008).  Linking Psychometric and Cognitive-Developmental Frameworks for Thinking About Intellectual Functioning.  In Raven, J. & Raven, J. (ed.), Uses and Abuses of Intelligence: Studies Advancing Spearman and Raven’s Quest for Non-Arbitrary Metrics. Royal Fireworks Press.

How to get someone’s g

“Intelligence”, “IQ”, “g” (due to Spearman), are terms that are bandied around.

The following may be helpful: the gist of how to calculate someone’s g score, which is often used as the measure of someone’s “intelligence”.

For example, that’s the “IQ”/”intelligence” referred to in the recentish BBC article on research linking childhood intelligence and adult vegetarianism (clever children grow into clever vegetarian adults).

  1. Give hundreds or thousands of people a dozen tests of ability.
  2. Zap everyone’s scores with PCA or factor analysis.
  3. g is the first component and usually explains around half the variance.  Here’s an example genre of analysis of g with other facets to psychometric intelligence.
  4. Use the component to calculate a score.  For factor analysis there are many ways to do this, e.g. Thompson’s scores, Bartlett’s weighted least-squares.  The gist is that for each person you compute a weighted sum of their scores, where the weights are a function of how loaded the particular test score was on g.
  5. To get something resembling an IQ score, scale it so it has a mean of 100 and an SD of 15.
  6. Talk about it as if it were a substantive psychological construct, rather than a statistical artefact 😉

What is this mysterious g thing?